数据库第三章习题参考答案

合集下载

数据库第三章所有例题参考答案

数据库第三章所有例题参考答案

11级信管,保密,图档上机考试题目与参考答案3.3Simple Select Statements1.EXAMPLE 3.3.1find the aid values and names of agents that are based in New York. select aid, aname from agents where city=’New York’;2.EXAMPLE3.3.3Retrieve all pid values of parts for which orders are placed.select distinct pid from orders;3.EXAMPLE 3.3.4retrieve all customer-agent name pairs, (cname, aname), where the customer places an order through the agent.select distinct ame,agents.anamefrom customers,orders,agentswhere customers.cid=orders.cid and orders.aid=agents.aid;4.EXAMPLE 3.3.6all pairs of customers based in the same city.select c1.cid, c2.cidfrom customers c1, customers c2where c1.city = c2.city and c1.cid < c2.cid;5.EXAMPLE 3.3.7find pid values of products that have been ordered by at least twocustomers.select distinct x1.pidfrom orders x1, orders x2where x1.pid = x2.pid and x1.cid < x2.cid;6.EXAMPLE 3.3.8Get cid values of customers who order a product for which an order is also placed by agent a06.select distinct y.cidfrom orders x, orders ywhere y.pid = x,pid and x.aid = ‘a06’;3.4Subqueries7.EXAMPLE 3.4.1Get cid values of customers who place orders with agents in Duluth or Dallas.select distinct cid from orderswhere aid in (select aid from agentswhere city= ‘Duluth’ or city = ‘Dallas’)8.EXAMPLE 3.4.2to retrieve all information concerning agents based in Duluth or Dallas (very close to the Subquery in the previous example).select * from agentswhere city in (‘Duluth’, ‘Dallas’ );or select *from agentswhere city = ‘Duluth’ or city = ‘Dallas’;9.EXAMPLE 3.4.3to determine the names and discounts of all customers who place orders through agents in Duluth or Dallas.select distinct cname, discnt from customerswhere cid in (select cid from orders where aid in(select aid from agents where city in (‘Duluth’, ‘Dallas’ ))); 10.EXAMPLE 3.4.4to find the names of customers who order product p05.select distinct cname from customers, orderswhere customers.cid = orders.cid and orders.pid = ‘p05’or select disti nct cname from customers where ‘p05’ in(select pid from orders where cid = customers.cid);11.EXAMPLE 3.4.5Get the names of customers who order product p07 from agent a03. select distinct cname from customerswhere cid in (select cid from orders where pid = ‘p07’ and aid = ‘a03’) 12.EXAMPLE 3.4.6to retrieve ordno values for all orders placed by customers in Duluth through agents in New York.select ordno from orders x where exists(select * from customers c, agents awhere c.cid = x.cid and a.aid = x.aid and c.city = ‘Duluth’ anda.city=‘New York’);13.EXAMPLE 3.4.7find aid values of agents with a minimum percent commission.select aid from agents where percent = (select min(percent) from agents);14.EXAMPLE 3.4.8find all customers who have the same discount as that of any of the customers in Dallas or Boston.select cid, cname from customerswhere discnt = some (select discnt from customerswhere city = ‘Dallas’ or city = ‘Boston’);15.EXAMPLE 3.4.9Get cid values of customers with discnt smaller than those of any customers who live in Duluth.select cid from customerswhere discnt <all (select discnt from customerswhere city = ‘Duluth’);16.EXAMPLE 3.4.10Retrieve all customer names where the customer places an order through agent a05.select distinct ame from customers cwhere exists (select * from orders xwhere c.cid = x.cid and x.aid = ‘a05’);or select distinct ame from customers c, orders xwhere c.cid = x.cid and x.ai d = ‘a05’ ;17.EXAMPLE 3.4.11Get cid values of customers who order both products p01 and p07. select distinct cid from orders xwhere pid = ‘p01’ and exsits (select * from orderswhere cid = x.cid and pid = ‘p07’);orselect distinct x.cid from orders x, orders ywhere x.pid = ‘p01’ and x.cid = y.cid and y.pid = ‘p07’;18.EXAMPLE 3.4.12Retrieve all customer names where the customer does not place an order through agent a05.select distinct ame from customers cwhere not exists (select * from orders xwhere c.cid = x.cid and x.aid = ‘a05’);19.EXAMPLE 3.4.13retrieving all customer names where the customer does not place an order through agent a05, but using the two equivalent NOT IN and <>ALLpredicates in place of NOT EXISTS.select distinct ame from customers cwhere c.cid not in (select cid from orders where aid = ‘a05’);or select ame from customers cwhere c.cid <>all (select cid from orders where aid = ‘a05’);20.EXAMPLE 3.4.14Find cid values of customers who do not place any order through agent a03.select distinct cid from orders xwhere not exists (select * from orderswhere cid = x.cid and aid = ‘a03’);orselect cid from customers cwhere not exists (select * from orderswhere cid = c.cid and aid = ‘a03’);21.EXAMPLE 3.4.15Retrieve the city names containing customers who order product p01. select distinct city from customers where cid in(select cid from orders where pid = ‘p01’);or select distinct city from customers where cid =some(select cid from orders where pid = ‘p01’);or select distinct city from customers c where exsits(select * from orders where cid = c.cid and pid = ‘p01’);or select distinct city from customers c, orders xwhere x.cid = c.cid and x.pid = ‘p01’;or select distinct city from customers c where ‘p01’ in(select pid from orders where cid = c.cid);3.5UNION Operators and FOR ALL Conditions 22.EXAMPLE 3.5.1to create a list of cities where either a customer or an agent, or both, is based.select city from customersunion select city from agents;23.EXAMPLE 3.5.2Get the cid values of customers who place orders with all agents based in New York.select c.cid from customers cwhere not exsits(select * from agents awhere a.city = ‘New York’ and not exsits(select * from orders xwhere x.cid = c.cid and x.aid = a.aid));24.EXAMPLE 3.5.3Get the aid values of agents in New York or Duluth who place orders forall products costing more than a dollar.select aid from agents awhere (a.city = ‘New York’ or a.city = ‘Duluth’)and not exsits(select p.pid from products pwhere p.price > 1.00 and not exsits(select * from orders xwhere x.pid = p.pid and x.aid = a.aid));25.EXAMPLE 3.5.4Find aid values of agents who place orders for product p01 as well as for all products costing more than a dollar.select a.aid from agents a where a.aid in(select aid from orders where pid = ‘p01’)and not exsits (select p.pid from products pwhere p.price > 1.00 and not exsits (select * from orders xwhere x.pid = p.pid and x.aid = a.aid));or select distinct y.aid from orders ywhere y.pid = ‘p01’ and not exsits(select p.pid from products pwhere p.price > 1.00 and not exsits(select * from orders xwhere x.pid = p.pid and x.aid = y.aid));26.EXAMPLE 3.5.6Find pid values of products supplied to all customers in Duluth.select pid from products pwhere not exsits(select c.cid from customers cwhere c.city = ‘Duluth’and not exists(select * from orders xwhere x.pid = p.pid and x.cid = c.cid));3.7 Set Functions in SQL27.EXAMPLE 3.7.1determine the total dollar amount of all orders.select sum(dollars) as totaldollars from orders28.EXAMPLE 3.7.2To determine the total quantity of product p03 that has been ordered. select sum(qty) as TOTAL from orders where pid=’p03’29.EXAMPLE 3.7.4Get the number of cities where customers are based.select count(distinct city) from customers30.EXAMPLE 3.7.5List the cid values of alt customers who have a discount less than the maximum discount.select cid from customerswhere discnt < (select max(discnt) from customers)31.EXAMPLE 3.7.6Find products ordered by at least two customers.select p.pid from products pwhere 2 <=(select count(distinct cid) from orders where pid=p.pid)图档的学生的上机考查的考题到此为止___________________________________________________________ ___________________________________________________________ 信管,保密的学生上机考查还包括下面的题目32.EXAMPLE 3.7.7Add a row with specified values for columns cid, cname, and city (c007, Windix, Dallas, null)to the customers table.insert into customers(cid, cname, city)values (‘c007’, ‘Windix’, ‘Dallas’)33.EXAMPLE 3.7.9After inserting the row (c007, Windix, Dallas, null) to the customers table in Example 3.7.7, assume that we wish to find the average discount of all customers.select avg(discnt) from customers3.8 Groups of Rows in SQL34.EXAMPLE 3.8.1to calculate the total product quantity ordered of each individual product by each individual agent.select pid, aid, sum(qty) as TOTAL from ordersgroup by pid, aid35.EXAMPLE 3.8.2Print out the agent name and agent identification number, and the product name and product identification number, together with the total quantity each agent supplies of that product to customers c002 and c003.select aname, a.aid, pname, p.pid, sum(qty)from orders x, products p, agents awhere x.pid = p.pid and x.aid = a.aid and x.cid in (‘c002’, ‘c003’)group by a.aid, a.aname, p.pid, p.pname36.EXAMPLE 3.8.3Print out all product and agent IDs and the total quantity ordered of the product by the agent, when this quantity exceeds 1000.select pid, aid, sum(qty) as TOTAL from ordersgroup by pid, aidhaving sum(qty) > 100037.EXAMPLE 3.8.4Provide pid values of all products purchased by at least two customers. select distinct pid from ordersgroup by pidhaving count(distinct cid) >= 23.9 A Complete Description of SQL Select38.EXAMPLE 3.9.1List all customers, agents, and the dollar sales for pairs of customers and agents, and order the result from largest to smallest sales totals. Retain only those pairs for which the dollar amount is at least equal to 900.00. select ame, c.cid, a.aname, a.aid, sum(dollars) as casalesfrom customers c, orders o, agents awhere c.cid = o.cid, and a.aid = o.aidgroup by ame, c.cid, a.aname, a.aidhaving sum(o.dollars) >= 900.00order by casales desc39.EXAMPLE 3.9.2listed the cid values of all customers with a discount less than the maximum discount.select cid from customerswhere discnt < (select max(discnt) from customers)40.EXAMPLE 3.9.3Retrieve the maximum discount of all customers.select max(discnt) from customers;select distinct discnt from customers cwhere discnt >= all (select discnt from customers dwhere d.cid<>c.cid)41.EXAMPLE 3.9.4Retrieve all data about customers whose cname begins with the letter “A”.select * from customers where cname like ‘A%’42.EXAMPLE 3.9.5Retrieve cid values of customers whose cname does not have a third letter equal to “%”.select cid from customers where cname not like ‘__[%]’43.EXAMPLE 3.9.6Retrieve cid values of customers whose cname begins “Tip_” and has an arbitrary number of characters following.select cid from customers where cname like ‘TIP\[_]%’44.EXAMPLE 3.9.7Retrieve cid values of customers whose cname starts with the sequence “ab\”.select cid from customers where cname like ‘ab\%’3.10 Insert, Update, and Delete Statements 45.EXAMPLE 3.10.1Add a row with specified values to the orders table, setting the qty and dollars columns null.insert into orders (ordno, month, cid, aid, pid)values (1107, ‘aug’, ‘c006’, ‘a04’, ‘p01’)46.EXAMPLE 3.10.2Create a new table called swcusts of Southwestern customers, and insert into it all customers from Dallas and Austin.create table swcusts (cid char(4) not null,cname varchar(13),city varchar(20),discnt real);insert into swcustsselect * from customerswhere city in (‘Dallas’, ‘Austin’)47.EXAMPLE 3.10.3Give all agents in New York a 10% raise in the percent commission they earn on an order.update agents set percent = 1.1 * percent where city = ‘New York’48.EXAMPLE 3.10.4Give all customers who have total orders of more than $1000 a 10% increase in the discnt.update agents set percent = 1.1 * discntwhere cid in(select cid from orders group by cid having sum(dollars) > 1000) 49.EXAMPLE 3.10.6Delete all agents in New York.delete from agents where city = ‘New York’50.EXAMPLE 3.10.7Delete all agents who have total orders of less than $600.Delete from agents where aid in(select aid from ordersGroup by aidHaving sum(dollars)<600)51.EXAMPLE 3.11.2Retrieve the names of customers who order products costing $0.50. delete from agents where aid in(select aid from orders group by aid having sum(dollars)<600)(完)。

(完整版)数据库课后习题及答案

(完整版)数据库课后习题及答案

第一章数据库系统概述选择题1实体-联系模型中,属性是指(C)A.客观存在的事物B.事物的具体描述C.事物的某一特征D.某一具体事件2对于现实世界中事物的特征,在E-R模型中使用(A)A属性描述B关键字描述C二维表格描述D实体描述3假设一个书店用这样一组属性描述图书(书号,书名,作者,出版社,出版日期),可以作为“键”的属性是(A)A书号B书名C作者D出版社4一名作家与他所出版过的书籍之间的联系类型是(B)A一对一B一对多C多对多D都不是5若无法确定哪个属性为某实体的键,则(A)A该实体没有键B必须增加一个属性作为该实体的键C取一个外关键字作为实体的键D该实体的所有属性构成键填空题1对于现实世界中事物的特征在E-R模型中使用属性进行描述2确定属性的两条基本原则是不可分和无关联3在描述实体集的所有属性中,可以唯一的标识每个实体的属性称为键4实体集之间联系的三种类型分别是1:1 、1:n 、和m:n5数据的完整性是指数据的正确性、有效性、相容性、和一致性简答题一、简述数据库的设计步骤答:1需求分析:对需要使用数据库系统来进行管理的现实世界中对象的业务流程、业务规则和所涉及的数据进行调查、分析和研究,充分理解现实世界中的实际问题和需求。

分析的策略:自下而上——静态需求、自上而下——动态需求2数据库概念设计:数据库概念设计是在需求分析的基础上,建立概念数据模型,用概念模型描述实际问题所涉及的数据及数据之间的联系。

3数据库逻辑设计:数据库逻辑设计是根据概念数据模型建立逻辑数据模型,逻辑数据模型是一种面向数据库系统的数据模型。

4数据库实现:依据关系模型,在数据库管理系统环境中建立数据库。

二、数据库的功能答:1提供数据定义语言,允许使用者建立新的数据库并建立数据的逻辑结构2提供数据查询语言3提供数据操纵语言4支持大量数据存储5控制并发访问三、数据库的特点答:1数据结构化。

2数据高度共享、低冗余度、易扩充3数据独立4数据由数据库管理系统统一管理和控制:(1)数据安全性(2)数据完整性(3)并发控制(4)数据库恢复第二章关系模型和关系数据库选择题1把E-R模型转换为关系模型时,A实体(“一”方)和B实体(“多”方)之间一对多联系在关系模型中是通过(A)来实现的A将A关系的关键字放入B关系中B建立新的关键字C建立新的联系D建立新的实体2关系S和关系R集合运算的结果中既包含S中元组也包含R中元组,但不包含重复元组,这种集合运算称为(A)A并运算B交运算C差运算D积运算3设有关系R1和R2,经过关系运算得到结果S,则S是一个(D)A字段B记录C数据库D关系4关系数据操作的基础是关系代数。

数据库系统基本教学教程第三章答案解析

数据库系统基本教学教程第三章答案解析

Exercise 3.1.1Answers for this exercise may vary because of different interpretations.Some possible FDs:Social Security number → nameArea code → stateStreet address, city, state → zipcodePossible keys:{Social Security number, street address, city, state, area code, phone number}Need street address, city, state to uniquely determine location. A person could havemultiple addresses. The same is true for phones. These days, a person could have alandline and a cellular phoneExercise 3.1.2Answers for this exercise may vary because of different interpretationsSome possible FDs:ID → x-position, y-position, z-positionID → x-velocity, y-velocity, z-velocityx-position, y-position, z-position → IDPossible keys:{ID}{x-position, y-position, z-position}The reason why the positions would be a key is no two molecules can occupy the same point. Exercise 3.1.3aThe superkeys are any subset that contains A1. Thus, there are 2(n-1) such subsets, since each of the n-1 attributes A2 through A n may independently be chosen in or out.Exercise 3.1.3bThe superkeys are any subset that contains A1 or A2. There are 2(n-1) such subsets when considering A1 and the n-1 attributes A2 through A n. There are 2(n-2) such subsets when considering A2 and the n-2 attributes A3 through A n. We do not count A1 in these subsets because they are already counted in the first group of subsets. The total number of subsets is 2(n-1) + 2(n-2).Exercise 3.1.3cThe superkeys are any subset that contains {A1,A2} or {A3,A4}. There are 2(n-2) such subsets when considering {A1,A2} and the n-2 attributes A3 through A n. There are 2(n-2) – 2(n-4) such subsets when considering {A3,A4} and attributes A5 through A n along with the individual attributes A1 and A2. We get the 2(n-4) term because we have to discard the subsets that contain the key {A1,A2} to avoid double counting. The total number of subsets is 2(n-2) + 2(n-2) – 2(n-4).Exercise 3.1.3dThe superkeys are any subset that contains {A1,A2} or {A1,A3}. There are 2(n-2) such subsets when considering {A1,A2} and the n-2 attributes A3 through A n. There are 2(n-3) such subsets when considering {A1,A3} and the n-3 attributes A4 through A n We do not count A2 in these subsets because they are already counted in the first group of subsets. The total number of subsets is 2(n-2) + 2(n-3).Exercise 3.2.1aWe could try inference rules to deduce new dependencies until we are satisfied we have them all. A more systematic way is to consider the closures of all 15 nonempty sets of attributes.For the single attributes we have {A}+ = A, {B}+ = B, {C}+ = ACD, and {D}+ = AD. Thus, the only new dependency we get with a single attribute on the left is C A.Now consider pairs of attributes:{AB}+ = ABCD, so we get new dependency AB→D. {AC}+ = ACD, and AC→D is nontrivial. {AD}+ = AD, so nothing new. {BC}+ = ABCD, so we get BC→A, and BC→D. {BD}+ = ABCD, giving us BD→A and BD→C. {CD}+ = ACD, giving CD→A.For the triples of attributes, {ACD}+ = ACD, but the closures of the other sets are each ABCD. Thus, we get new dependencies ABC→D, ABD→C, and BCD→A.Since {ABCD}+ = ABCD, we get no new dependencies.The collection of 11 new dependencies mentioned above are:C→A, AB→D, AC→D, BC→A, BC→D, BD→A, BD→C, CD→A, ABC→D, ABD→C, and BCD→A.Exercise 3.2.1bFrom the analysis of closures above, we find that AB, BC, and BD are keys. All other sets either do not have ABCD as the closure or contain one of these three sets.Exercise 3.2.1cThe superkeys are all those that contain one of those three keys. That is, a superkey that is not a key must contain B and more than one of A, C, and D. Thus, the (proper) superkeys are ABC, ABD, BCD, and ABCD.Exercise 3.2.2ai) For the single attributes we have {A}+ = ABCD, {B}+ = BCD, {C}+ = C, and {D}+ = D. Thus, the new dependencies are A→C and A→D.Now consider pairs of attributes:{AB}+ = ABCD, {AC}+ = ABCD, {AD}+ = ABCD, {BC}+ = BCD, {BD}+ = BCD, {CD}+ = CD. Thus the new dependencies are AB→C, AB→D, AC→B, AC→D, AD→B, AD→C, BC→D and BD→C.For the triples of attributes, {BCD}+ = BCD, but the closures of the other sets are each ABCD. Thus, we get new dependencies ABC→D, ABD→C, and ACD→B.Since {ABCD}+ = ABCD, we get no new dependencies.The collection of 13 new dependencies mentioned above are:A→C, A→D, AB→C, AB→D, AC→B, AC→D, AD→B, AD→C, BC→D, BD→C, ABC→D, ABD→C and ACD→B.ii) For the single attributes we have {A}+ = A, {B}+ = B, {C}+ = C, and {D}+ = D. Thus, there are no new dependencies.Now consider pairs of attributes:{AB}+ = ABCD, {AC}+ = AC, {AD}+ = ABCD, {BC}+ = ABCD, {BD}+ = BD, {CD}+ = ABCD. Thus the new dependencies are AB→D, AD→C, BC→A and CD→B.For the triples of attributes, all the closures of the sets are each ABCD. Thus, we get new dependencies ABC→D, ABD→C, ACD→B and BCD→A.Since {ABCD}+ = ABCD, we get no new dependencies.The collection of 8 new dependencies mentioned above are:AB→D, AD→C, BC→A, CD→B, ABC→D, ABD→C, ACD→B and BCD→A.iii) For the single attributes we have {A}+ = ABCD, {B}+ = ABCD, {C}+ = ABCD, and {D}+ = ABCD. Thus, the new dependencies are A→C, A→D, B→D, B→A, C→A, C→B, D→B and D→C.Since all the single attributes’ closures are ABCD, any superset of the single attributes will also lead to a closure of ABCD. Knowing this, we can enumerate the rest of the new dependencies.The collection of 24 new dependencies mentioned above are:A→C, A→D, B→D, B→A, C→A, C→B, D→B, D→C, AB→C, AB→D, AC→B, AC→D, AD→B, AD→C, BC→A, BC→D, BD→A, BD→C, CD→A, CD→B, ABC→D, ABD→C, ACD→B and BCD→A.Exercise 3.2.2bi) From the analysis of closures in 3.2.2a(i), we find that the only key is A. All other sets either do not have ABCD as the closure or contain A.ii) From the analysis of closures 3.2.2a(ii), we find that AB, AD, BC, and CD are keys. All other sets either do not have ABCD as the closure or contain one of these four sets.iii) From the analysis of closures 3.2.2a(iii), we find that A, B, C and D are keys. All other sets either do not have ABCD as the closure or contain one of these four sets.Exercise 3.2.2ci) The superkeys are all those sets that contain one of the keys in 3.2.2b(i). The superkeys are AB, AC, AD, ABC, ABD, ACD, BCD and ABCD.ii) The superkeys are all those sets that contain one of the keys in 3.2.2b(ii). The superkeys are ABC, ABD, ACD, BCD and ABCD.iii) The superkeys are all those sets that contain one of the keys in 3.2.2b(iii). The superkeys are AB, AC, AD, BC, BD, CD, ABC, ABD, ACD, BCD and ABCD.Exercise 3.2.3aSince A1A2…A n C contains A1A2…A n, then the closure of A1A2…A n C contains B. Thus it follows that A1A2…A n C→B.Exercise 3.2.3bFrom 3.2.3a, we know that A1A2…A n C→B. Using the concept of trivial dependencies, we can show that A1A2…A n C→C. Thus A1A2…A n C→BC.Exercise 3.2.3cFrom A1A2…A n E1E2…E j, we know that the closure contains B1B2…B m because of the FD A1A2…A n→ B1B2…B m. The B1B2…B m and the E1E2…E j combine to form the C1C2…C k. Thus the closure of A1A2…A n E1E2…E j containsD as well. Thus, A1A2…A n E1E2…E j→D.Exercise 3.2.3dFrom A1A2…A n C1C2…C k, we know that the closure contains B1B2…B m because of the FD A1A2…A n→ B1B2…B m. The C1C2…C k also tell us that the closure of A1A2…A n C1C2…C k contains D1D2…D j. Thus, A1A2…A n C1C2…C k→B1B2…B k D1D2…D j.Exercise 3.2.4aIf attribute A represented Social Security Number and B represented a person’s name, then we would assume A→B but B→A would not be valid because there may be many people with the same name and different Social Security Numbers.Exercise 3.2.4bLet attribute A represent Social Security Number, B represent gender and C represent name. Surely Social Security Number and gender can uniquely identify a person’s name (i.e.AB→C). A Social Security Number can also uniquely identify a person’s name (i.e. A→C). However, gender does not uniquely determine a name (i.e. B→C is not valid).Exercise 3.2.4cLet attribute A represent latitude and B represent longitude. Together, both attributes can uniquely determine C, a point on the world map (i.e. AB→C). However, neither A nor B can uniquely identify a point (i.e. A→C and B→C are not valid).Exercise 3.2.5Given a relation with attributes A1A2…A n, we are told that there are no functional dependencies of the form B1B2…B n-1→C where B1B2…B n-1 is n-1 of the attributes from A1A2…A n and C is the remaining attribute from A1A2…A n. In this case, the set B1B2…B n-1 and any subset do not functionally determine C. Thus the only functional dependencies that we canmake are ones where C is on both the left and right hand sides. All of these functional dependencies would be trivial and thus the relation has no nontrivial FD’s.Exercise 3.2.6Let’s prove this by using the contrapositive. We wish to show that if X+ is not a subset of Y+, then it must be that X is not a subset of Y.If X+ is not a subset of Y+, there must be attributes A1A2…A n in X+ that are not in Y+. If any of these attributes were originally in X, then we are done because Y does not contain any of the A1A2…A n. However, if the A1A2…A n were added by the closure, then we must examine the case further. Assume that there was some FD C1C2…C m→A1A2…A j where A1A2…A j is some subset of A1A2…A n. It must be then that C1C2…C m or some subset of C1C2…C m is in X. However, the attributes C1C2…C m cannot be in Y because we assumed that attributes A1A2…A n are only in X+ and are not in Y+. Thus, X is not a subset of Y.By proving the contrapositive, we have also proved if X ⊆ Y, then X+⊆ Y+.Exercise 3.2.7The algorithm to find X+ is outlined on pg. 76. Using that algorithm, we can prove that(X+)+ = X+. We will do this by using a proof by contradiction.Suppose that (X+)+≠ X+. Then for (X+)+, it must be that some FD allowed additional attributes to be added to the original set X+. For example, X+→ A where A is some attribute not in X+. However, if this were the case, then X+ would not be the closure of X. The closure of X would have to include A as well. This contradicts the fact that we were given the closure of X, X+. Therefore, it must be that (X+)+ = X+ or else X+ is not the closure of X.Exercise 3.2.8aIf all sets of attributes are closed, then there cannot be any nontrivial functional dependencies. Suppose A1A2...A n→B is a nontrivial dependency. Then {A1A2...A n}+ contains B and thus A1A2...A n is not closed.Exercise 3.2.8bIf the only closed sets are ø and {A,B,C,D}, then the following FDs hold:A→B A→C A→DB→A B→C B→DC→A C→B C→DD→A D→B D→CAB→C AB→DAC→B AC→DAD→B AD→CBC→A BC→DBD→A BD→CCD→A CD→BABC→DABD→CACD→BBCD→AExercise 3.2.8cIf the only closed sets are ø, {A,B} and {A,B,C,D}, then the following FDs hold:A→BB→AC→A C→B C→DD→A D→B D→CAC→B AC→DAD→B AD→CBC→A BC→DBD→A BD→CCD→A CD→BABC→DABD→CACD→BBCD→AExercise 3.2.9We can think of this problem as a situation where the attributes A,B,C represent cities and the functional dependencies represent one way paths between the cities. The minimal bases are the minimal number of pathways that are needed to connect the cities. We do not want to create another roadway if the two cities are already connected.The systematic way to do this would be to check all possible sets of the pathways. However, we can simplify the situation by noting that it takes more than two pathways to visit the two other cities and come back. Also, if we find a set of pathways that is minimal, adding additional pathways will not create another minimal set.The two sets of minimal bases that were given in example 3.11 are:{A→B, B→C, C→A}{A→B, B→A, B→C, C→B}The additional sets of minimal bases are:{C→B, B→A, A→C}{A→B, A→C, B→A, C→A}{A→C, B→C, C→A, C→B}Exercise 3.2.10aWe need to compute the closures of all subsets of {ABC}, although there is no need to think about the empty set or the set of all three attributes. Here are the calculations for the remaining six sets:{A}+=A{B}+=B{C}+=ACE{AB}+=ABCDE{AC}+=ACE{BC}+=ABCDEWe ignore D and E, so a basis for the resulting functional dependencies for ABC is: C→A and AB→C. Note that BC->A is true, but follows logically from C->A, and therefore may be omitted from our list.Exercise 3.2.10bWe need to compute the closures of all subsets of {ABC}, although there is no need to think about the empty set or the set of all three attributes. Here are the calculations for the remaining six sets:{A}+=AD{B}+=B{C}+=C{AB}+=ABDE{AC}+=ABCDE{BC}+=BCWe ignore D and E, so a basis for the resulting functional dependencies for ABC is: AC→B.Exercise 3.2.10cWe need to compute the closures of all subsets of {ABC}, although there is no need to think about the empty set or the set of all three attributes. Here are the calculations for the remaining six sets:{A}+=A{B}+=B{C}+=C{AB}+=ABD{AC}+=ABCDE{BC}+=ABCDEWe ignore D and E, so a basis for the resulting functional dependencies for ABC is: AC→B and BC→A.Exercise 3.2.10dWe need to compute the closures of all subsets of {ABC}, although there is no need to think about the empty set or the set of all three attributes. Here are the calculations for the remaining six sets:{A}+=ABCDE{B}+=ABCDE{C}+=ABCDE{AB}+=ABCDE{AC}+=ABCDE{BC}+=ABCDEWe ignore D and E, so a basis for the resulting functional dependencies for ABC is: A→B,B→C and C→A.Exercise 3.2.11For step one of Algorithm 3.7, suppose we have the FD ABC→DE. We want to use Armstrong’s Axioms to show that ABC→D and ABC→E follow. Surely the functional dependencies DE→D and DE→E hold because they are trivial and follow the reflexivity property. Using the transitivity rule, we can derive the FD ABC→D from the FDs ABC→DE and DE→D. Likewise, we can do the same for ABC→DE and DE→E and derive the FD ABC→E.For steps two through four of Algorithm 3.7, suppose we have the initial set of attributes of the closure as ABC. Suppose also that we have FDs C→D and D→E. According to Algorithm 3.7, the closure should become ABCDE. Taking the FD C→D and augmenting both sides with attributes AB we get the FD ABC→ABD. We can use the splitting method in step one to get the FD ABC→D. Since D is not in the closure, we can add attribute D. Taking the FD D→E and augmenting both sides with attributes ABC we get the FD ABCD→ABCDE. Using again the splitting method in step one we get the FD ABCD→E. Since E is not in the closure, we can add attribute E.Given a set of FDs, we can prove that a FD F follows by taking the closure of the left side of FD F. The steps to compute the closure in Algorithm 3.7 can be mimicked by Armstrong’s axioms and thus we can prove F from the given set of FDs using Armstrong’s axioms.Exercise 3.3.1aIn the solution to Exercise 3.2.1 we found that there are 14 nontrivial dependencies, including the three given ones and eleven derived dependencies. They are: C→A, C→D, D→A, AB→D, AB→ C, AC→D, BC→A, BC→D, BD→A, BD→C, CD→A, ABC→D, ABD→C, and BCD→A.We also learned that the three keys were AB, BC, and BD. Thus, any dependency above that does not have one of these pairs on the left is a BCNF violation. These are: C→A, C→D, D→A, AC→D, and CD→A.One choice is to decompose using the violation C→D. Using the above FDs, we get ACD and BC as decomposed relations. BC is surely in BCNF, since any two-attribute relation is. Using Algorithm 3.12 to discover the projection of FDs on relation ACD, we discover that ACD is not in BCNF since C is its only key. However, D→A is a dependency that holds in ABCD and therefore holds in ACD. We must further decompose ACD into AD and CD. Thus, the three relations of the decomposition are BC, AD, and CD.Exercise 3.3.1bBy computing the closures of all 15 nonempty subsets of ABCD, we can find all the nontrivial FDs. They are B→C, B→D, AB→C, AB→D, BC→D, BD→C, ABC→D and ABD→C. From the closures we can also deduce that the only key is AB. Thus, any dependency above that does not contain AB on the left is a BCNF violation. These are: B→C, B→D, BC→D and BD→C.One choice is to decompose using the violation B→C. Using the above FDs, we get BCD and AB as decomposed relations. AB is surely in BCNF, since any two-attribute relation is. Using Algorithm 3.12 to discover the projection of FDs on relation BCD, we discover that BCD is in BCNF since B is its only key and the projected FDs all have B on the left side. Thus the two relations of the decomposition are AB and BCD.Exercise 3.3.1cIn the solution to Exercise 3.2.2(ii), we found that there are 12 nontrivial dependencies, including the four given ones and the eight derived ones. They are AB→C, BC→D, CD→A, AD→B, AB→D, AD→C, BC→A, CD→B, ABC→D, ABD→C, ACD→B and BCD→A.We also found out that the keys are AB, AD, BC, and CD. Thus, any dependency above that does not have one of these pairs on the left is a BCNF violation. However, all of the FDs contain a key on the left so there are no BCNF violations.No decomposition is necessary since all the FDs do not violate BCNF.Exercise 3.3.1dIn the solution to Exercise 3.2.2(iii), we found that there are 28 nontrivial dependencies, including the four given ones and the 24 derived ones. They are A→B, B→C, C→D, D→A,A→C, A→D, B→D, B→A, C→A, C→B, D→B, D→C, AB→C, AB→D, AC→B, AC→D, AD→B, AD→C, BC→A, BC→D, BD→A, BD→C, CD→A, CD→B, ABC→D, ABD→C, ACD→B and BCD→A.We also found out that the keys are A,B,C,D. Thus, any dependency above that does not have one of these attributes on the left is a BCNF violation. However, all of the FDs contain a key on the left so there are no BCNF violations.No decomposition is necessary since all the FDs do not violate BCNF.Exercise 3.3.1eBy computing the closures of all 31 nonempty subsets of ABCDE, we can find all the nontrivial FDs. They are AB→C, DE→C, B→D, AB→D, BC→D, BE→C, BE→D, ABC→D, ABD→C, ABE→C, ABE→D, ADE→C, BCE→D, BDE→C, ABCE→D, and ABDE→C. From the closures we can also deduce that the only key is ABE. Thus, any dependency above that does not contain ABE on the left is a BCNF violation. These are: AB→C, DE→C, B→D, AB→D, BC→D, BE→C,BE→D, ABC→D, ABD→C, ADE→C, BCE→D and BDE→C.One choice is to decompose using the violation AB→C. Using the above FDs, we get ABCD and ABE as decomposed relations. Using Algorithm 3.12 to discover the projection of FDs on relation ABCD, we discover that ABCD is not in BCNF since AB is its only key and the FDB→D follows for ABCD. Using violation B→D to further decompose, we get BD and ABC as decomposed relations. BD is in BCNF because it is a two-attribute relation. Using Algorithm 3.12 again, we discover that ABC is in BCNF since AB is the only key and AB→C is the only nontrivial FD. Going back to relation ABE, following Algorithm 3.12 tells us that ABE is in BCNF because there are no keys and no nontrivial FDs. Thus the three relations of the decomposition are ABC, BD and ABE.Exercise 3.3.1fBy computing the closures of all 31 nonempty subsets of ABCDE, we can find all the nontrivial FDs. They are: C→B, C→D, C→E, D→B, D→E, AB→C, AB→D, AB→E, AC→B, AC→D, AC→E, AD→B, AD→C, AD→E, BC→D, BC→E, BD→E, CD→B, CD→E, CE→B, CE→D, DE→B, ABC→D, ABC→E, ABD→C, ABD→E, ABE→C, ABE→D, ACD→B, ACD→E, ACE→B, ACE→D, ADE→B, ADE→C, BCD→E, BCE→D, CDE→B, ABCD→E, ABCE→D, ABDE→C and ACDE→B. From the closures we can also deduce that the keys are AB, AC and AD. Thus, any dependency above that does not contain one of the above pairs on the left is a BCNF violation. These are: C→B, C→D, C→E, D→B, D→E, BC→D, BC→E, BD→E, CD→B, CD→E, CE→B, CE→D, DE→B, BCD→E, BCE→D and CDE→B.One choice is to decompose using the violation D→B. Using the above FDs, we get BDE and ABC as decomposed relations. Using Algorithm 3.12 to discover the projection of FDs on relation BDE, we discover that BDE is in BCNF since D, BD, DE are the only keys and all the projected FDs contain D, BD, or DE in the left side. Going back to relation ABC, following Algorithm 3.12 tells us that ABC is not in BCNF because since AB and AC are its only keys and the FD C→B follows for ABC. Using violation C→B to further decompose, we get BC and AC as decomposed relations. Both BC and AC are in BCNF because they are two-attribute relations. Thus the three relations of the decomposition are BDE, BC and AC.Exercise 3.3.2Yes, we will get the same result. Both A→B and A→BC have A on the left side and part of the process of decomposition involves finding {A}+ to form one decomposed relation and A plus the rest of the attributes not in {A}+ as the second relation. Both cases yield the same decomposed relations.Exercise 3.3.3Yes, we will still get the same result. Both A→B and A→BC have A on the left side and part of the process of decomposition involves finding {A}+ to form one decomposed relation and A plus the rest of the attributes not in {A}+ as the second relation. Both cases yield the same decomposed relations.Exercise 3.3.4This is taken from Example 3.21 pg. 95.Suppose that an instance of relation R only contains two tuples.The projections of R onto the relations with schemas {A,B} and {B,C} are:If we do a natural join on the two projections, we will get:The result of the natural join is not equal to the original relation R.Exercise 3.4.1aThis is the initial tableau:A.Since there is not an unsubscripted row, the decomposition for R is not lossless for this set of FDs.We can use the final tableau as an instance of R as an example for why the join is not lossless. The projected relations are:The joined relation is:The joined relation has three more tuples than the original tableau.Exercise 3.4.1bThis is the initial tableau:This is the final tableau after applying FDs AC→E and BC→DSince there is an unsubscripted row, the decomposition for R is lossless for this set of FDs. Exercise 3.4.1cThis is the initial tableau:This is the final tableau after applying FDs A→D, D→E and B→D.Since there is an unsubscripted row, the decomposition for R is lossless for this set of FDs. Exercise 3.4.1dThis is the initial tableau:This is the final tableau after applying FDs A→D, CD→E and E→DSince there is an unsubscripted row, the decomposition for R is lossless for this set of FDs. Exercise 3.4.2When we decompose a relation into BCNF, we will project the FDs onto the decomposed relations to get new sets of FDs. These dependencies are preserved if the union of these new sets is equivalent to the original set of FDs.For the FDs of 3.4.1a, the dependencies are not preserved. The union of the new sets of FDs is CE→A. However, the FD B→E is not in the union and cannot be derived. Thus the two sets of FDs are not equivalent.For the FDs of 3.4.1b, the dependencies are preserved. The union of the new sets of FDs is AC→E and BC→D. This is precisely the same as the original set of FDs and thus the two sets of FDs are equivalent.For the FDs of 3.4.1c, the dependencies are not preserved. The union of the new sets of FDs is B→D and A→E. The FDs A→D and D→E are not in the union and cannot be derived. Thus the two sets of FDs are not equivalent.For the FDs of 3.4.1d, the dependencies are not preserved. The union of the new sets of FDs is AC→E. However, the FDs A→D, CD→E and E→D are not in the union and cannot be derived. Thus the two sets of FDs are not equivalent.Exercise 3.5.1aIn the solution to Exercise 3.3.1a we found that there are 14 nontrivial dependencies. They are: C→A, C→D, D→A, AB→D, AB→ C, AC→D, BC→A, BC→D, BD→A, BD→C, CD→A, ABC→D, ABD→C, and BCD→A.We also learned that the three keys were AB, BC, and BD. Since all the attributes on the right sides of the FDs are prime, there are no 3NF violations.Since there are no 3NF violations, it is not necessary to decompose the relation.Exercise 3.5.1bIn the solution to Exercise 3.3.1b we found that there are 8 nontrivial dependencies. They are B→C, B→D, AB→C, AB→D, BC→D, BD→C, ABC→D and ABD→C.We also found out that the only key is AB. FDs where the left side is not a superkey or the attributes on the right are not part of some key are 3NF violations. The 3NF violations areB→C, B→D, BC→D and BD→C.Using algorithm 3.26, we can decompose into relations using the minimal basis B→C andB→D. The resulting decomposed relations would be BC and BD. However, none of these two sets of attributes is a superkey. Thus we add relation AB to the result. The final set of decomposed relations is BC, BD and AB.Exercise 3.5.1cIn the solution to Exercise 3.3.1c we found that there are 12 nontrivial dependencies. They are AB→C, BC→D, CD→A, AD→B, AB→D, AD→C, BC→A, CD→B, ABC→D, ABD→C, ACD→B and BCD→A.We also found out that the keys are AB, AD, BC, and CD. Since all the attributes on the right sides of the FDs are prime, there are no 3NF violations.Since there are no 3NF violations, it is not necessary to decompose the relation.Exercise 3.5.1dIn the solution to Exercise 3.3.1d we found that there are 28 nontrivial dependencies. They are A→B, B→C, C→D, D→A, A→C, A→D, B→D, B→A, C→A, C→B, D→B, D→C, AB→C, AB→D, AC→B, AC→D, AD→B, AD→C, BC→A, BC→D, BD→A, BD→C, CD→A, CD→B, ABC→D, ABD→C, ACD→B and BCD→A.We also found out that the keys are A,B,C,D. Since all the attributes on the right sides of the FDs are prime, there are no 3NF violations.Since there are no 3NF violations, it is not necessary to decompose the relation.Exercise 3.5.1eIn the solution to Exercise 3.3.1e we found that there are 16 nontrivial dependencies. They are AB→C, DE→C, B→D, AB→D, BC→D, BE→C, BE→D, ABC→D, ABD→C, ABE→C, ABE→D, ADE→C, BCE→D, BDE→C, ABCE→D, and ABDE→C.We also found out that the only key is ABE. FDs where the left side is not a superkey or the attributes on the right are not part of some key are 3NF violations. The 3NF violations are AB→C, DE→C, B→D, AB→D, BC→D, BE→C, BE→D, ABC→D, ABD→C, ADE→C, BCE→D and BDE→C.Using algorithm 3.26, we can decompose into relations using the minimal basis AB→C,DE→C and B→D. The resulting decomposed relations would be ABC, CDE and BD. However, none of these three sets of attributes is a superkey. Thus we add relation ABE to the result. The final set of decomposed relations is ABC, CDE, BD and ABE.Exercise 3.5.1fIn the solution to Exercise 3.3.1f we found that there are 41 nontrivial dependencies. They are: C→B, C→D, C→E, D→B, D→E, AB→C, AB→D, AB→E, AC→B, AC→D, AC→E, AD→B, AD→C, AD→E, BC→D, BC→E, BD→E, CD→B, CD→E, CE→B, CE→D, DE→B, ABC→D, ABC→E, ABD→C, ABD→E, ABE→C, ABE→D, ACD→B, ACD→E, ACE→B, ACE→D, ADE→B, ADE→C, BCD→E, BCE→D, CDE→B, ABCD→E, ABCE→D, ABDE→C and ACDE→B.We also found out that the keys are AB, AC and AD. FDs where the left side is not a superkey or the attributes on the right are not part of some key are 3NF violations. The 3NF violations are C→E, D→E, BC→E, BD→E, CD→E and BCD→E.Using algorithm 3.26, we can decompose into relations using the minimal basis AB→C, C→D, D→B and D→E. The resulting decomposed relations would be ABC, CD, BD and DE. Since relation ABC contains a key, we can stop with the decomposition. The final set of decomposed relations is ABC, CD, BD and DE.Exercise 3.5.2aThe usual procedure to find the keys would be to take the closure of all 63 nonempty subsets. However, if we notice that none of the right sides of the FDs contains attributes H and S. Thus we know that attributes H and S must be part of any key. We eventually will find out that HS is the only key for the Courses relation.Exercise 3.5.2b。

数据库概论第1-3章习题参考答案

数据库概论第1-3章习题参考答案

第1章绪论习题参考答案1、试述数据、数据库、数据库管理系统、数据库系统的概念。

(参见P3、4、5页)参考答案:描述事物的符号记录称为数据;数据库是长期储存在计算机内的、有组织的、可共享的数据集合;数据库管理系统是位于用户与操作系统之间的一层数据管理软件; 数据库系统是指在计算机系统中引入数据库后的系统,一般由数据库、数据库管理系统(及其开发工具)、应用系统、数据库管理员和用户构成。

2.使用数据库系统有什么好处?(参见P12页)参考答案:数据库系统使信息系统从以加工数据的程序为中心转向围绕共享的数据库为中心的阶段,这样既便于数据的集中管理,又有利于应用程序的研制和维护,提高了数据的利用率和相容性,提高了决策的可靠性。

3.试述文件系统与数据库系统的区别和联系。

(8、9、10页)参考答案:1)数据结构化是数据库与文件系统的根本区别。

在文件系统中,相互独立的文件的记录内部是有结构的,管其记录内部已有了某些结构,但记录之间没有联系。

数据库系统实现整体数据的结构化,是数据库的主要特征之一。

2)在文件系统中,数据的最小存取单位是记录,粒度不能细到数据项。

而在数据库系统中,存取数据的方式也很灵活,可以存取数据库中的某一个数据项、一组数据项一个记录或或一组记录。

3)文件系统中的文件是为某一特定应用服务的,文件的逻辑结构对该应用程序来说是优化的,因此要想对现有的数据再增加一些新的应用会很困难,系统不容易扩充。

而在数据库系统中数据不再针对某一应用,而是面向全组织,具有整体的结构化。

5.试述数据库系统的特点。

(9、10、11页)参考答案:数据结构化;数据的共享性高、冗余度低、易扩充;数据独立性高;数据由DBMS统一管理和控制。

6.数据库管理系统的主要功能有哪些? (4页)参考答案:数据定义功能、数据操纵功能、数据库的运行管理、数据库的建立和维护功能。

7.试述数据模型的概念(13页)、数据模型的作用、数据模型的三个要素。

数据库 第三章习题参考答案

数据库 第三章习题参考答案

三、设计题1.(1)SELECT BAuth FROM Book, PublishWHERE Book.PNo= Publish.PNo AND BName=’操作系统’ AND PName=’高等教育出版社’(2)查找为作者“张欣”出版全部“小说”类图书的出版社的电话。

SELECT PTel FROM Book, PublishWHERE Book.PNo= Publish.PNo AND BType =’小说’ AND BAuth=’张欣’(3)查询“电子工业出版社”出版的“计算机”类图书的价格,同时输出出版社名称及图书类别。

SELECT BPrice, PName, BType FROM Book, PublishWHERE Book.PNo= Publish.PNo AND PName =’电子工业出版社’ AND BType =’计算机’(4)查找比“人民邮电出版社”出版的“高等数学”价格低的同名书的有关信息。

SELECT * FROM BookWHERE BName =’高等数学’AND BPrice<ANY(SELECT BPrice FROM Book,PublishWHERE Book.PNo= Publish.PNo AND PName =’人民邮电出版社’ AND BName =’高等数学’)AND PName <>’人民邮电出版社’(5)查找书名中有“计算机”一词的图书的书名及作者。

SELECT BName, BAuth FROM BookWHERE BName LIKE’%计算机%’(6)在“图书”表中增加“出版时间”(BDate)项,其数据类型为日期型。

ALTER TABLE BookADD BDate datetime(7)在“图书”表中以“作者”建立一个索引。

CREATE INDEX Name ON Book(BAuth) desc2.(1)建立存书表和销售表。

【精选】数据库第三章课后习题

【精选】数据库第三章课后习题
order by grade
• 14、 • (1)GRANT SELECT ON 职工,部门TO 王明 • (2) GRANT INSERT,DELETE ON 职工,部门TO
李勇
• (3) GRANT SELECT ON 职工WHEN USER() = NAME TO ALL
• (4) GRANT SELECT,UPDATE(工资) ON 职工 TO 刘星
• 7、视图的优点 • 视图能够简化用户的操作 • 视图使用户能以多种角度看待同一数据 • 视图对重构数据库提供了一定程度的逻辑
独立性; • 视图能够对机密数据提供安全保护。
• 8、所有的视图是否都可以更新?
• 不是。视图是不实际存储数据的虚表,因 此对视图的更新,最终要转换为对基本表 的更新。因为有些视图的更新不能惟一有 意义地转换成对相应基本表的更新,所以 ,并不是所有的视图都是可更新的。
SPJ TO 李天明;
• 13、 • (1)INSERT INTO SC(Sno,Cno,Grade)
VALUES("2000012", "1128", NULL); • (2)SELECT Sno,Cno
FROM SC
WHERE Grade IS NULL;
• (3)SELECT cname,grade FROM course,Sc WHERE o=o AND cname="英语"
• (1) SELECT DIST PNO,QTY FROM SPQ
• (2) SELECT DIST * FROM SPQ WHERE SNO="S1‘
• 12、 • (1)GRANT INSERT
ON TABLE S TO 张勇

数据库系统基础教程第三章答案

数据库系统基础教程第三章答案

Exercise 3.1.1Answers for this exercise may vary because of different interpretations.Some possible FDs:Social Security number → nameArea code → stateStreet address, city, state → zipcodePossible keys:{Social Security number, street address, city, state, area code, phone number}Need street address, city, state to uniquely determine location. A person couldhave multiple addresses. The same is true for phones. These days, a person couldhave a landline and a cellular phoneExercise 3.1.2Answers for this exercise may vary because of different interpretationsSome possible FDs:ID → x-position, y-position, z-positionID → x-velocity, y-velocity, z-velocityx-position, y-position, z-position → IDPossible keys:{ID}{x-position, y-position, z-position}The reason why the positions would be a key is no two molecules can occupy the same point.Exercise 3.1.3aThe superkeys are any subset that contains A1. Thus, there are 2(n-1) such subsets, since each of the n-1 attributes A2 through A n may independently be chosen in or out.Exercise 3.1.3bThe superkeys are any subset that contains A1 or A2. There are 2(n-1) such subsets when considering A1 and the n-1 attributes A2 through A n. There are 2(n-2) such subsets when considering A2 and the n-2 attributes A3 through A n. We do not count A1 in these subsets because they are already counted in the first group of subsets. The total number of subsets is 2(n-1) + 2(n-2).Exercise 3.1.3cThe superkeys are any subset that contains {A1,A2} or {A3,A4}. There are 2(n-2) such subsets when considering {A1,A2} and the n-2 attributes A3 through A n. There are 2(n-2) – 2(n-4) such subsets when considering {A3,A4} and attributes A5 through A n along with the individual attributes A1 and A2. We get the 2(n-4) term because we have to discard the subsets that contain the key {A1,A2} to avoid double counting. The total number of subsets is 2(n-2) +2(n-2) – 2(n-4).Exercise 3.1.3dThe superkeys are any subset that contains {A1,A2} or {A1,A3}. There are 2(n-2) such subsets when considering {A1,A2} and the n-2 attributes A3 through A n. There are 2(n-3) such subsets when considering {A1,A3} and the n-3 attributes A4 through A n We do not count A2 in these subsets because they are already counted in the first group of subsets. The total number of subsets is 2(n-2) + 2(n-3).Exercise 3.2.1aWe could try inference rules to deduce new dependencies until we are satisfied we have them all. A more systematic way is to consider the closures of all 15 nonempty sets of attributes.For the single attributes we have {A}+ = A, {B}+ = B, {C}+ = ACD, and {D}+ = AD. Thus, the only new dependency we get with a single attribute on the left is C→A.Now consider pairs of attributes:{AB}+ = ABCD, so we get new dependency AB→D. {AC}+ = ACD, and AC→D is nontrivial. {AD}+= AD, so nothing new. {BC}+ = ABCD, so we get BC→A, and BC→D. {BD}+ = ABCD, giving us BD→A and BD→C. {CD}+ = ACD, giving CD→A.For the triples of attributes, {ACD}+ = ACD, but the closures of the other sets are each ABCD. Thus, we get new dependencies ABC→D, ABD→C, and BCD→A.Since {ABCD}+ = ABCD, we get no new dependencies.The collection of 11 new dependencies mentioned above are:C→A, AB→D, AC→D, BC→A, BC→D, BD→A, BD→C, CD→A, ABC→D, ABD→C, and BCD→A.Exercise 3.2.1bFrom the analysis of closures above, we find that AB, BC, and BD are keys. All other sets either do not have ABCD as the closure or contain one of these three sets.Exercise 3.2.1cThe superkeys are all those that contain one of those three keys. That is, a superkeythat is not a key must contain B and more than one of A, C, and D. Thus, the (proper) superkeys are ABC, ABD, BCD, and ABCD.Exercise 3.2.2ai) For the single attributes we have {A}+ = ABCD, {B}+ = BCD, {C}+ = C, and {D}+ = D. Thus, the new dependencies are A→C and A→D.Now consider pairs of attributes:{AB}+ = ABCD, {AC}+ = ABCD, {AD}+ = ABCD, {BC}+ = BCD, {BD}+ = BCD, {CD}+ = CD. Thus the new dependencies are AB→C, AB→D, AC→B, AC→D, AD→B, AD→C, BC→D and BD→C.For the triples of attributes, {BCD}+ = BCD, but the closures of the other sets are each ABCD. Thus, we get new dependencies ABC→D, ABD→C, and ACD→B.Since {ABCD}+ = ABCD, we get no new dependencies.The collection of 13 new dependencies mentioned above are:A→C, A→D, AB→C, AB→D, AC→B, AC→D, AD→B, AD→C, BC→D, BD→C, ABC→D, ABD→C and ACD→B.ii) For the single attributes we have {A}+ = A, {B}+ = B, {C}+ = C, and {D}+ = D. Thus, there are no new dependencies.Now consider pairs of attributes:{AB}+ = ABCD, {AC}+ = AC, {AD}+ = ABCD, {BC}+ = ABCD, {BD}+ = BD, {CD}+ = ABCD. Thus the new dependencies are AB→D, AD→C, BC→A and CD→B.For the triples of attributes, all the closures of the sets are each ABCD. Thus, we get new dependencies ABC→D, ABD→C, ACD→B and BCD→A.Since {ABCD}+ = ABCD, we get no new dependencies.The collection of 8 new dependencies mentioned above are:AB→D, AD→C, BC→A, CD→B, ABC→D, ABD→C, ACD→B and BCD→A.iii) For the single attributes we have {A}+ = ABCD, {B}+ = ABCD, {C}+ = ABCD, and {D}+ = ABCD. Thus, the new dependencies are A→C, A→D, B→D, B→A, C→A, C→B, D→B and D→C.Since all the single attributes’ closures are ABCD, any superset of the singleattributes will also lead to a closure of ABCD. Knowing this, we can enumerate the restof the new dependencies.The collection of 24 new dependencies mentioned above are:A→C, A→D, B→D, B→A, C→A, C→B, D→B, D→C, AB→C, AB→D, AC→B, AC→D, AD→B, AD→C, BC→A, BC→D, BD→A, BD→C, CD→A, CD→B, ABC→D, ABD→C, ACD→B and BCD→A.Exercise 3.2.2bi) From the analysis of closures in 3.2.2a(i), we find that the only key is A. All other sets either do not have ABCD as the closure or contain A.ii) From the analysis of closures 3.2.2a(ii), we find that AB, AD, BC, and CD are keys.All other sets either do not have ABCD as the closure or contain one of these four sets.iii) From the analysis of closures 3.2.2a(iii), we find that A, B, C and D are keys. All other sets either do not have ABCD as the closure or contain one of these four sets.Exercise 3.2.2ci) The superkeys are all those sets that contain one of the keys in 3.2.2b(i). The superkeys are AB, AC, AD, ABC, ABD, ACD, BCD and ABCD.ii) The superkeys are all those sets that contain one of the keys in 3.2.2b(ii). The superkeys are ABC, ABD, ACD, BCD and ABCD.iii) The superkeys are all those sets that contain one of the keys in 3.2.2b(iii). The superkeys are AB, AC, AD, BC, BD, CD, ABC, ABD, ACD, BCD and ABCD.Exercise 3.2.3aSince A1A2…A n C contains A1A2…A n, then the closure of A1A2…A n C contains B. Thus it follows that A1A2…A n C→B.Exercise 3.2.3bFrom 3.2.3a, we know that A1A2…A n C→B. Using the concept of trivial dependencies, we can show that A1A2…A n C→C. Thus A1A2…A n C→BC.Exercise 3.2.3cFrom A1A2…A n E1E2…E j, we know that the closure contains B1B2…B m because of the FD A1A2…A n→B1B2…B m. The B1B2…B m and the E1E2…E j combine to form the C1C2…C k. Thus the closure ofA1A2…A n E1E2…E j contains D as well. Thus, A1A2…A n E1E2…E j→D.Exercise 3.2.3dFrom A1A2…A n C1C2…C k, we know that the closure contains B1B2…B m because of the FD A1A2…A n→B1B2…B m. The C1C2…C k also tell us that the closure of A1A2…A n C1C2…C k contains D1D2…D j. Thus, A1A2…A n C1C2…C k→B1B2…B k D1D2…D j.Exercise 3.2.4aIf attribute A represented Social Security Number and B represented a person’s name,then we would assume A→B but B→A would not be valid because there may be many peoplewith the same name and different Social Security Numbers.Exercise 3.2.4bLet attribute A represent Social Security Number, B represent gender and C represent name. Surely Social Security Number and gender can uniquely identify a person’s name . AB→C).A Social Security Number can also uniquely identify a person’s name . A→C). However, gender does not uniquely determine a name . B→C is not valid).Exercise 3.2.4cLet attribute A represent latitude and B represent longitude. Together, both attributes can uniquely determine C, a point on the world map . AB→C). However, neither A nor B can uniquely identify a point . A→C and B→C are not valid).Exercise 3.2.5Given a relation with attributes A1A2…A n, we are told that there are no functional dependencies of the form B1B2…B n-1→C where B1B2…B n-1 is n-1 of the attributes from A1A2…A n and C is the remaining attribute from A1A2…A n. In this case, the set B1B2…B n-1 and any subset do not functionally determine C. Thus the only functional dependencies that we can make are ones where C is on both the left and right hand sides. All of these functional dependencies would be trivial and thus the relation has no nontrivial FD’s.Exercise 3.2.6Let’s prove this by using the contrapositive. We wish to show that if X+ is not a subset of Y+, then it must be that X is not a subset of Y.If X+ is not a subset of Y+, there must be attributes A1A2…A n in X+ that are not in Y+. If any of these attributes were originally in X, then we are done because Y does not contain any of the A1A2…A n. However, if the A1A2…A n were added by the closure, then we must examine the case further. Assume that there was some FD C1C2…C m→A1A2…A j where A1A2…A j is some subset of A1A2…A n. It must be then that C1C2…C m or some subset of C1C2…C m is in X. However, the attributes C1C2…C m cannot be in Y because we assumed that attributes A1A2…A n are only in X+ and are not in Y+. Thus, X is not a subset of Y.By proving the contrapositive, we have also proved if X ⊆ Y, then X+⊆ Y+.Exercise 3.2.7The algorithm to find X+ is outlined on pg. 76. Using that algorithm, we can prove that(X+)+ = X+. We will do this by using a proof by contradiction.Suppose that (X+)+≠ X+. Then for (X+)+, it must be that some FD allowed additional attributes to be added to the original set X+. For example, X+→ A where A is some attribute not in X+. However, if this were the case, then X+ would not be the closure of X. The closure of X would have to include A as well. This contradicts the fact that we were given the closure of X, X+. Therefore, it must be that (X+)+ = X+ or else X+ is not the closure of X.Exercise 3.2.8aIf all sets of attributes are closed, then there cannot be any nontrivial functional dependencies. Suppose A1A2...A n→B is a nontrivial dependency. Then {A1A2...A n}+ contains B and thus A1A2...A n is not closed.Exercise 3.2.8bIf the only closed sets are ø and {A,B,C,D}, then the following FDs hold:A→B A→C A→DB→A B→C B→DC→A C→B C→DD→A D→B D→CAB→C AB→DAC→B AC→DAD→B AD→CBC→A BC→DBD→A BD→CCD→A CD→BABC→DABD→CACD→BBCD→AExercise 3.2.8cIf the only closed sets are ø, {A,B} and {A,B,C,D}, then the following FDs hold:A→BB→AC→A C→B C→DD→A D→B D→CAC→B AC→DAD→B AD→CBC→A BC→DBD→A BD→CCD→A CD→BABC→DABD→CACD→BBCD→AExercise 3.2.9We can think of this problem as a situation where the attributes A,B,C represent cities and the functional dependencies represent one way paths between the cities. The minimal bases are the minimal number of pathways that are needed to connect the cities. We do not want to create another roadway if the two cities are already connected.The systematic way to do this would be to check all possible sets of the pathways. However, we can simplify the situation by noting that it takes more than two pathways to visit the two other cities and come back. Also, if we find a set of pathways that is minimal, adding additional pathways will not create another minimal set.The two sets of minimal bases that were given in example are:{A→B, B→C, C→A}{A→B, B→A, B→C, C→B}The additional sets of minimal bases are:{C→B, B→A, A→C}{A→B, A→C, B→A, C→A}{A→C, B→C, C→A, C→B}Exercise 3.2.10aWe need to compute the closures of all subsets of {ABC}, although there is no need to think about the empty set or the set of all three attributes. Here are the calculations for the remaining six sets:{A}+=A{B}+=B{C}+=ACE{AB}+=ABCDE{AC}+=ACE{BC}+=ABCDEWe ignore D and E, so a basis for the resulting functional dependencies for ABC is: C→A and AB→C. Note that BC->A is true, but follows logically from C->A, and therefore may be omitted from our list.Exercise 3.2.10bWe need to compute the closures of all subsets of {ABC}, although there is no need tothink about the empty set or the set of all three attributes. Here are the calculationsfor the remaining six sets:{A}+=AD{B}+=B{C}+=C{AB}+=ABDE{AC}+=ABCDE{BC}+=BCWe ignore D and E, so a basis for the resulting functional dependencies for ABC is: AC→B.Exercise 3.2.10cWe need to compute the closures of all subsets of {ABC}, although there is no need tothink about the empty set or the set of all three attributes. Here are the calculationsfor the remaining six sets:{A}+=A{B}+=B{C}+=C{AB}+=ABD{AC}+=ABCDE{BC}+=ABCDEWe ignore D and E, so a basis for the resulting functional dependencies for ABC is: AC→B and BC→A.Exercise 3.2.10dWe need to compute the closures of all subsets of {ABC}, although there is no need tothink about the empty set or the set of all three attributes. Here are the calculationsfor the remaining six sets:{A}+=ABCDE{B}+=ABCDE{C}+=ABCDE{AB}+=ABCDE{AC}+=ABCDE{BC}+=ABCDEWe ignore D and E, so a basis for the resulting functional dependencies for ABC is: A→B, B→C and C→A.Exercise 3.2.11For step one of Algorithm , suppose we have the FD ABC→DE. We want to use Armstrong’s Axioms to show that ABC→D and ABC→E follow. Surely the functional dependencies DE→Dand DE→E hold because they are trivial and follow the reflexivity property. Using the transitivity rule, we can derive the FD ABC→D from the FDs ABC→DE and DE→D. Likewise, we can do the same for ABC→DE and DE→E and derive the FD ABC→E.For steps two through four of Algorithm , suppose we have the initial set of attributesof the closure as ABC. Suppose also that we have FDs C→D and D→E. According toAlgorithm , the closure should become ABCDE. Taking the FD C→D and augmenting both sides with attributes AB we get the FD ABC→ABD. We can use the splitting method in step one to get the FD ABC→D. Since D is not in the closure, we can add attribute D. Taking the FDD→E and augmenting both sides with attributes ABC we get the FD ABCD→ABCDE. Using again the splitting method in step one we get the FD ABCD→E. Since E is not in the closure, we can add attribute E.Given a set of FDs, we can prove that a FD F follows by taking the closure of the left side of FD F. The steps to compute the closure in Algorithm can be mimicked by Armstrong’s axioms and thus we can prove F from the given set of FDs using Armstrong’s axioms.Exercise 3.3.1aIn the solution to Exercise 3.2.1 we found that there are 14 nontrivial dependencies, including the three given ones and eleven derived dependencies. They are: C→A, C→D,D→A, AB→D, AB→ C, AC→D, BC→A, BC→D, BD→A, BD→C, CD→A, ABC→D, ABD→C, and BCD→A.We also learned that the three keys were AB, BC, and BD. Thus, any dependency above that does not have one of these pairs on the left is a BCNF violation. These are: C→A, C→D,D→A, AC→D, and CD→A.One choice is to decompose using the violation C→D. Using the above FDs, we get ACD and BC as decomposed relations. BC is surely in BCNF, since any two-attribute relation is. Using Algorithm to discover the projection of FDs on relation ACD, we discover that ACDis not in BCNF since C is its only key. However, D→A is a dependency that holds in ABCD and therefore holds in ACD. We must further decompose ACD into AD and CD. Thus, the three relations of the decomposition are BC, AD, and CD.Exercise 3.3.1bBy computing the closures of all 15 nonempty subsets of ABCD, we can find all thenontrivial FDs. They are B→C, B→D, AB→C, AB→D, BC→D, BD→C, ABC→D and ABD→C. From the closures we can also deduce that the only key is AB. Thus, any dependency above that does not contain AB on the left is a BCNF violation. These are: B→C, B→D, BC→D andBD→C.One choice is to decompose using the violation B→C. Using the above FDs, we get BCD and AB as decomposed relations. AB is surely in BCNF, since any two-attribute relation is. Using Algorithm to discover the projection of FDs on relation BCD, we discover that BCDis in BCNF since B is its only key and the projected FDs all have B on the left side. Thus the two relations of the decomposition are AB and BCD.Exercise 3.3.1cIn the solution to Exercise 3.2.2(ii), we found that there are 12 nontrivial dependencies, including the four given ones and the eight derived ones. They are AB→C, BC→D, CD→A, AD→B, AB→D, AD→C, BC→A, CD→B, ABC→D, ABD→C, ACD→B and BCD→A.We also found out that the keys are AB, AD, BC, and CD. Thus, any dependency above that does not have one of these pairs on the left is a BCNF violation. However, all of the FDs contain a key on the left so there are no BCNF violations.No decomposition is necessary since all the FDs do not violate BCNF.Exercise 3.3.1dIn the solution to Exercise 3.2.2(iii), we found that there are 28 nontrivial dependencies, including the four given ones and the 24 derived ones. They are A→B, B→C, C→D, D→A, A→C, A→D, B→D, B→A, C→A, C→B, D→B, D→C, AB→C, AB→D, AC→B, AC→D,AD→B, AD→C, BC→A, BC→D, BD→A, BD→C, CD→A, CD→B, ABC→D, ABD→C, ACD→B and BCD→A.We also found out that the keys are A,B,C,D. Thus, any dependency above that does nothave one of these attributes on the left is a BCNF violation. However, all of the FDs contain a key on the left so there are no BCNF violations.No decomposition is necessary since all the FDs do not violate BCNF.Exercise 3.3.1eBy computing the closures of all 31 nonempty subsets of ABCDE, we can find all the nontrivial FDs. They are AB→C, DE→C, B→D, AB→D, BC→D, BE→C, BE→D, ABC→D, ABD→C, ABE→C, ABE→D, ADE→C, BCE→D, BDE→C, ABCE→D, and ABDE→C. From the closures we canalso deduce that the only key is ABE. Thus, any dependency above that does not contain ABE on the left is a BCNF violation. These are: AB→C, DE→C, B→D, AB→D, BC→D, BE→C, BE→D, ABC→D, ABD→C, ADE→C, BCE→D and BDE→C.One choice is to decompose using the violation AB→C. Using the above FDs, we get ABCDand ABE as decomposed relations. Using Algorithm to discover the projection of FDs on relation ABCD, we discover that ABCD is not in BCNF since AB is its only key and the FDB→D follows for ABCD. Using violation B→D to further decompose, we get BD and ABC as decomposed relations. BD is in BCNF because it is a two-attribute relation. Using Algorithm again, we discover that ABC is in BCNF since AB is the only key and AB→C isthe only nontrivial FD. Going back to relation ABE, following Algorithm tells us that ABE is in BCNF because there are no keys and no nontrivial FDs. Thus the three relationsof the decomposition are ABC, BD and ABE.Exercise 3.3.1fBy computing the closures of all 31 nonempty subsets of ABCDE, we can find all the nontrivial FDs. They are: C→B, C→D, C→E, D→B, D→E, AB→C, AB→D, AB→E, AC→B, AC→D, AC→E, AD→B, AD→C, AD→E, BC→D, BC→E, BD→E, CD→B, CD→E, CE→B, CE→D, DE→B,ABC→D, ABC→E, ABD→C, ABD→E, ABE→C, ABE→D, ACD→B, ACD→E, ACE→B, ACE→D, ADE→B, ADE→C, BCD→E, BCE→D, CDE→B, ABCD→E, ABCE→D, ABDE→C and ACDE→B. From the closures we can also deduce that the keys are AB, AC and AD. Thus, any dependency above that does not contain one of the above pairs on the left is a BCNF violation. These are: C→B, C→D, C→E, D→B, D→E, BC→D, BC→E, BD→E, CD→B, CD→E, CE→B, CE→D, DE→B, BCD→E, BCE→D and CDE→B.One choice is to decompose using the violation D→B. Using the above FDs, we get BDE and ABC as decomposed relations. Using Algorithm to discover the projection of FDs onrelation BDE, we discover that BDE is in BCNF since D, BD, DE are the only keys and all the projected FDs contain D, BD, or DE in the left side. Going back to relation ABC, following Algorithm tells us that ABC is not in BCNF because since AB and AC are itsonly keys and the FD C→B follows for ABC. Using violation C→B to further decompose, we get BC and AC as decomposed relations. Both BC and AC are in BCNF because they are two-attribute relations. Thus the three relations of the decomposition are BDE, BC and AC.Exercise 3.3.2Yes, we will get the same result. Both A→B and A→BC have A on the left side and part of the process of decomposition involves finding {A}+ to form one decomposed relation and A plus the rest of the attributes not in {A}+ as the second relation. Both cases yield the same decomposed relations.Exercise 3.3.3Yes, we will still get the same result. Both A→B and A→BC have A on the left side and part of the process of decomposition involves finding {A}+ to form one decomposedrelation and A plus the rest of the attributes not in {A}+ as the second relation. Both cases yield the same decomposed relations.Exercise 3.3.4This is taken from Example pg. 95.Suppose that an instance of relation R only contains two tuples.A B C1 2 3425The projections of R onto the relations with schemas {A,B} and {B,C} are:A B1 2 42If we do a natural join on the two projections, we will get:A B C1 2 3 1 2 5 4 2 3 425The result of the natural join is not equal to the original relation R.Exercise 3.4.1aThis is the initial tableau:A B C D Ea b c d 1 e 1 a 1 b c d e 1 ab 1cd 1e→A.A B C D Ea b c d 1 e 1 a b c d e 1 ab 1cd 1eSince there is not an unsubscripted row, the decomposition for R is not lossless for this set of FDs.We can use the final tableau as an instance of R as an example for why the join is not lossless. The projected relations are:B C 2 3 25A B Ca b ca b1 cB C Db c d1b c db1 c d1A C Ea c e1a c eThe joined relation is:A B C D Ea b c d1 e1a b c d e1a b1 c d1 e1a b c d1 ea b c d ea b1 c d1 eThe joined relation has three more tuples than the original tableau. Exercise 3.4.1bThis is the initial tableau:A B C D Ea b c d1 e1a1 b c d e1a b1 c d1 eThis is the final tableau after applying FDs AC→E and BC→DA B C D Ea b c d ea1 b c d e1a b1 c d1 eSince there is an unsubscripted row, the decomposition for R is lossless for this set of FDs.Exercise 3.4.1cThis is the initial tableau:A B C D Ea b c d1 e1a1 b c d e1a b1 c d1 eThis is the final tableau after applying FDs A→D, D→E and B→D.A B C D Ea b c d ea1 b c d ea b1 c d eSince there is an unsubscripted row, the decomposition for R is lossless for this set of FDs.Exercise is the initial tableau:A B C D Ea b c d1 e1a1 b c d e1a b1 c d1 eThis is the final tableau after applying FDs A→D, CD→E and E→DA B C D Ea b c d ea1 b c d ea b1 c d eSince there is an unsubscripted row, the decomposition for R is lossless for this set of FDs.Exercise we decompose a relation into BCNF, we will project the FDs onto the decomposed relations to get new sets of FDs. These dependencies are preserved if the union of these new sets is equivalent to the original set of FDs.For the FDs of the dependencies are not preserved. The union of the new sets of FDs is CE→A. However, the FD B→E is not in the union and cannot be derived. Thus the two sets of FDs are not equivalent.For the FDs of the dependencies are preserved. The union of the new sets of FDs is AC→E and BC→D. This is precisely the same as the original set of FDs and thus the two sets of FDs are equivalent.For the FDs of the dependencies are not preserved. The union of the new sets of FDs isB→D and A→E. The FDs A→D and D→E are not in the union and cannot be derived. Thus the two sets of FDs are not equivalent.For the FDs of the dependencies are not preserved. The union of the new sets of FDs is AC→E. However, the FDs A→D, CD→E and E→D are not in the union and cannot be derived. Thus the two sets of FDs are not equivalent.Exercise the solution to Exercise we found that there are 14 nontrivial dependencies. They are: C→A, C→D, D→A, AB→D, AB→ C, AC→D, BC→A, BC→D, BD→A, BD→C, CD→A,ABC→D, ABD→C, and BCD→A.We also learned that the three keys were AB, BC, and BD. Since all the attributes on the right sides of the FDs are prime, there are no 3NF violations.Since there are no 3NF violations, it is not necessary to decompose the relation.Exercise the solution to Exercise we found that there are 8 nontrivial dependencies. They are B→C, B→D, AB→C, AB→D, BC→D, BD→C, ABC→D and ABD→C.We also found out that the only key is AB. FDs where the left side is not a superkey or the attributes on the right are not part of some key are 3NF violations. The 3NF violations are B→C, B→D, BC→D and BD→C.Using algorithm , we can decompose into relations using the minimal basis B→C and B→D. The resulting decomposed relations would be BC and BD. However, none of these two sets of attributes is a superkey. Thus we add relation AB to the result. The final set of decomposed relations is BC, BD and AB.Exercise the solution to Exercise we found that there are 12 nontrivial dependencies. They are AB→C, BC→D, CD→A, AD→B, AB→D, AD→C, BC→A, CD→B, ABC→D, ABD→C, ACD→B and BCD→A.We also found out that the keys are AB, AD, BC, and CD. Since all the attributes on the right sides of the FDs are prime, there are no 3NF violations.Since there are no 3NF violations, it is not necessary to decompose the relation.Exercise the solution to Exercise we found that there are 28 nontrivial dependencies. They are A→B, B→C, C→D, D→A, A→C, A→D, B→D, B→A, C→A, C→B, D→B, D→C, AB→C, AB→D, AC→B, AC→D, AD→B, AD→C, BC→A, BC→D, BD→A, BD→C, CD→A, CD→B, ABC→D,ABD→C, ACD→B and BCD→A.We also found out that the keys are A,B,C,D. Since all the attributes on the right sides of the FDs are prime, there are no 3NF violations.Since there are no 3NF violations, it is not necessary to decompose the relation.Exercise the solution to Exercise we found that there are 16 nontrivial dependencies. They are AB→C, DE→C, B→D, AB→D, BC→D, BE→C, BE→D, ABC→D, ABD→C, ABE→C, ABE→D, ADE→C, BCE→D, BDE→C, ABCE→D, and ABDE→C.We also found out that the only key is ABE. FDs where the left side is not a superkey or the attributes on the right are not part of some key are 3NF violations. The 3NF violations are AB→C, DE→C, B→D, AB→D, BC→D, BE→C, BE→D, ABC→D, ABD→C, ADE→C, BCE→D and BDE→C.Using algorithm , we can decompose into relations using the minimal basis AB→C, DE→C and B→D. The resulting decomposed relations would be ABC, CDE and BD. However, none of these three sets of attributes is a superkey. Thus we add relation ABE to the result. The final set of decomposed relations is ABC, CDE, BD and ABE.Exercise the solution to Exercise we found that there are 41 nontrivial dependencies. They are: C→B, C→D, C→E, D→B, D→E, AB→C, AB→D, AB→E, AC→B, AC→D, AC→E, AD→B, AD→C, AD→E, BC→D, BC→E, BD→E, CD→B, CD→E, CE→B, CE→D, DE→B, ABC→D, ABC→E, ABD→C, ABD→E, ABE→C, ABE→D, ACD→B, ACD→E, ACE→B, ACE→D, ADE→B, ADE→C, BCD→E, BCE→D, CDE→B, ABCD→E, ABCE→D, ABDE→C and ACDE→B.We also found out that the keys are AB, AC and AD. FDs where the left side is not a superkey or the attributes on the right are not part of some key are 3NF violations. The 3NF violations are C→E, D→E, BC→E, BD→E, CD→E and BCD→E.Using algorithm , we can decompose into relations using the minimal basis AB→C, C→D,D→B and D→E. The resulting decomposed relations would be ABC, CD, BD and DE. Since。

数据库1-3章习题参考答案

数据库1-3章习题参考答案

第二章 习题
二、多项选择题 5、下列关系代数运算中,要求是相容关系的是( ) A. 投影 B. 并 C.交 D.差 6、 关系模型的完整性规则包括( )。 A. 实体完整性规则 B.参照完整性规则 C.安全性规则 D.用户定义的完整性规 则 7.扩充关系代数 包括 ( )。 A. 外联接 B. 除 C.外部并 D.联接 8、自然联接运算是由( )操作组合而成 A. 投影 B.选择 C.笛卡儿积 D.并 9、关系模型是由( )组成 A. 数据结构 B.数据描述语言 C.数据操作 D.完 整性规则
6、试述过程性DML与非过程性DML的区别 。 用户使用过程性DML编程时,不仅需要指出 “做什么”,而且还需指出“怎么做”。用 户使用非过程性DML编程时,则需指出“做 什么”,不需指出“怎么做” 。
三、应用题
1、为某百货公司设计一个E-R模型。 某百货公司管辖若干个连锁商店,每家商 店经营若干种商品,每家商店有若干职工, 但每个职工只能服务于一家商店。 试画出反映商店、商品、职工之间联系的 E-R模型,并将其转换成关系模式集。
1、在关系中能唯一标识元组的属性集为( D )。 A.外部键 B.候选键 C.主键 D.超键
2、在实体中有属性可作为键而选定其中一个时,称
为该实体的 ( C )。 A.外部键 B.候选键 C.主键 D.主属性
3、若某属性虽非该实体的主键,却是另一实体的主
键,称该属性为( A )。 A.外部键 B.候选键 C.主键 D.主属性
第一章 习题
6、数据独立性与数据联系这两个概念有什 么区别? 7、试述DBMS在用户访问数据库过程中所 起的作用。
8、试述过程性DML与非过程性DML的区别 。
三、应用题
1、为某百货公司设计一个E-R模型。 某百货公司管辖若干个连锁商店,每家商 店经营若干种商品,每家商店有若干职工, 但每个职工只能服务于一家商店。 试画出反映商店、商品、职工之间联系的 E-R模型,并将其转换成关系模式集。
  1. 1、下载文档前请自行甄别文档内容的完整性,平台不提供额外的编辑、内容补充、找答案等附加服务。
  2. 2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
  3. 3、如文档侵犯您的权益,请联系客服反馈,我们会尽快为您处理(人工客服工作时间:9:00-18:30)。

3-2 对于教务管理数据库的三个基本表
S(SNO,SNAME, SEX, AGE,SDEPT)
SC(SNO,CNO,GRADE)
C(CNO,CNAME,CDEPT,TNAME)
试用SQL的查询语句表达下列查询:
⑴检索LIU老师所授课程的课程号和课程名。

⑵检索年龄大于23岁的男学生的学号和姓名。

⑶检索学号为6的学生所学课程的课程名和任课教师名。

⑷检索至少选修LIU老师所授课程中一门课程的女学生姓名。

⑸检索WANG同学不学的课程的课程号。

⑹检索至少选修两门课程的学生学号。

⑺检索全部学生都选修的课程的课程号与课程名。

⑻检索选修课程包含LIU老师所授课程的学生学号。

解:
⑴ SELECT C#,CNAME
FROM C
WHERE TEACHER=’LIU’;
⑵ SELECT S#,SNAME
FROM S
WHERE AGE>23 AND SEX=’M’;
⑶ SELECT CNAME,TEACHER
FROM SC,C
WHERE #=# AND S#=’200915146’
⑷ SELECT SNAME (连接查询方式)
FROM S,SC,C
WHERE #=# AND #=# AND SEX=’F’ AND TEACHER=’LIU’;
或:
SELECT SNAME (嵌套查询方式)
FROM S
WHERE SEX=’F’AND S# IN
(SELECT S#
FROM SC
WHERE C# IN (SELECT C#
FROM C
WHERE TEACHER=’LIU’))
或:
SELECT SNAME (存在量词方式)
FROM S
WHERE SEX=’F’ AND EXIS TS(SELECT*
FROM SC
WHERE #=#
AND EXISTS(SELECT *
FROM C
WHERE #=# AND TEACHER=’LIU’))
⑸ SELECT C#
FROM C
WHERE NOT EXISTS
(SELECT *
FROM S,SC
WHERE #=# AND #=# AND SNAME=’WANG));
⑹ SELECT DISTINCT #
FROM SC AS X,SC AS Y
WHERE #=# AND #!=#;
⑺ SELECT C#.CNAME
FROM C
WHERE NOT EXISTS (SELECT *
FROM S
WHERE NOT EXISTS
(SELECT *
FROM SC
WHERE S#=# AND C#=#));
⑻ SELECT DISTINCT S#
FROM SC AS X
WHERE NOT EXISTIS
(SELECT *
FROM C
WHERE TEACHER=’LIU’ AND NOT EXISTS
(SELECT *
FROM SC AS Y
WHERE #=# AND #=#));
3-3 试用SQL查询语句表达下列对题中教务管理数据库的三个基本表S、SC、C 查询:
⑴统计有学生选修的课程门数。

⑵求选修4号课程的学生的平均年龄。

⑶求LIU老师所授课程的每门课程的学生平均成绩。

⑷统计每门课程的学生选修人数(超过10人的课程才统计)。

要求输出课程号和选修人数,查询结果按人数降序排列,若人数相同,按课程号升序排列。

⑸检索学号比WANG同学大,而年龄比他小的学生姓名。

⑹检索姓名以WANG打头的所有学生的姓名和年龄。

⑺在SC中检索成绩为空值的学生学号和课程号。

⑻求年龄大于女同学平均年龄的男学生姓名和年龄。

⑼求年龄大于所有女同学年龄的男学生姓名和年龄。

解:
⑴ SELECT COUNT(DISTINCT C#)
FROM SC;
⑵ SELECT AVG(AGE)
FROM S,SC
WHERE #=# AND C#=’4’AND SEX=’F’;
⑶ SELECT #,AVG(GRADE)
FROM SC,C
WHERE #=# AND TEACHER=’LIU’;
⑷ SELECT C#,COUNT(S#)
FROM SC
GROUP BY C#
HAVING COUNT(*)>10
ORDER BY 2 DESC,1;
⑸ SELECT SNAME
FROM S
WHERE S#>ALL(SELECT S#
FROM S
WHERE SNAME=’WANG’
AND AGE<ALL(SELECT AGE
FROM S
WHERE SNAME=’WANG’);
⑹ SELECT SNAME,AGE
FROM S
WHERE SNAME LIKE ‘WANG%’
⑺ SELECT S#,C#
FROM SC
WHERE GRADE IS NULL;
⑻ SELECT SNAME,AGE
FROM S
WHERE SEX=’M’AND AGE>(SELECT AVG(AGE)
FROM S
WHERE SEX=’F’);
⑼ SELECT SNAME,AGE
FROM S
WHERE SEX=’M’AND AGE>ALL(SELECT AGE
FROM S
WHERE SEX=’F’);
3-4 试用SQL更新语句表达对给出的教务管理数据库中三个基本表S、SC、C进行如下更新操作:
⑴往基本表S中插入一个学生元组(‘3’,‘张晶’,21)。

⑵在基本表S中检索每一门课程成绩都大于等于80分的学生学号、姓名和性别,并把检索到的值送往另一个已存在的基本表STUDENT(SNO,SNAME,SEX)。

⑶在基本表SC中删除尚无成绩的选课元组。

⑷把张成民同学在SC中的选课记录全部删去。

⑸把选修高等数学课程中不及格的成绩全部改为空值。

⑹把低于总平均成绩的女同学成绩提高5%。

⑺在基本表SC中修改4号课程的成绩,若成绩小于等于75分时提高5%,若成绩大于75分时提高4%(用两个UPDATE语句实现)。

解:
⑴INSERT INTO S(S#,SNAME,AGE) VALUES(‘200912143’,’张晶’,21);
⑵INSERT INTO STUDENT (SNO,SNAME,SEX) SELECT S#,SNAME,SEX
FROM S
WHERE S# IN (SELECT S#
FROM SC
WHERE 80<=ALL(SELECT GRADE
FROM SC
GROUP BY S#));
⑶DELETE FROM SC
WHERE GRADE IS NULL;
⑷DELETE
FROM SC
WHERE S# IN(SELECT S#
FROM S
WHERE SNAME=’张成民’)
⑸UPDATE SC
SET GRADE=NULL
WHERE GRADE<60 AND C# IN(SELECT C# FROM C
WHERE CNAME=’高等数学’);
⑹UPDATE SC
SET GRADE=GRADE*
WHERE S# IN(SELECT S#
FROM S
WHERE SEX=’F’)
AND GRADE<(SELECT AVG(GRADE)
FROM SC);
⑺用两个UPDATE语句实现:
UPDATE SC
SET GRADE=GRADE*
WHERE C#=’4’AND GRADE>75;
UPDATE SC
SET GRADE=GRADE*
WHERE C#=’4’AND GRADE<=75;
注意:这两个UPDATE语句的顺序不能颠倒。

相关文档
最新文档