Lattice of Substitutions is a Heyting Algebra MML IdentifierHEYTING2.

合集下载

Let a, bbesets.Notethat{a, b}isfunction-likeandrelation-like. Let A, Bbesets.Observethat A

FORMALIZED MATHEMATICSVolume7,Number2,1998University of BiałystokLattice of Substitutions is a HeytingAlgebraAdam GrabowskiUniversity of BiałystokMML Identiﬁer:HEYTING2.The terminology and notation used in this paper have been introduced in the following articles:[2],[15],[1],[7],[13],[9],[3],[4],[10],[18],[5],[16],[17],[11], [14],[8],[12],and[6].1.PreliminariesWe adopt the following convention:V,C,x are sets and A,B are elements of SubstitutionSet(V,C).Let a,b be sets.Note that{ a,b }is function-like and relation-like.Let A,B be sets.Observe that A˙→B is functional.Next we state several propositions:(1)For all non empty sets V,C there exists an element f of V˙→C such thatf=∅.(2)For all sets a,b such that b∈SubstitutionSet(V,C)and a∈b holds a isaﬁnite function.(3)For every element f of V˙→C and for every set g such that g⊆f holdsg∈V˙→C.(4)V˙→C⊆2[:V,C:].(5)If V isﬁnite and C isﬁnite,then V˙→C isﬁnite.One can check that there exists a set which is functional,ﬁnite,and non empty.323c 1998University of BiałystokISSN1426–2630324adam grabowski2.Some Properties of Sets of SubstitutionsOne can prove the following four propositions:(6)For everyﬁnite element a of V˙→C holds{a}∈SubstitutionSet(V,C).(7)If A B=A,then for every set a such that a∈A there exists a set bsuch that b∈B and b⊆a.(8)Ifµ(A B)=A,then for every set a such that a∈A there exists a setb such that b∈B and b⊆a.(9)If for every set a such that a∈A there exists a set b such that b∈Band b⊆a,thenµ(A B)=A.Let V be a set,let C be aﬁnite set,and let A be an element of Fin(V˙→C).The functor Involved A is deﬁned by:(Def.1)x∈Involved A iﬀthere exists aﬁnite function f such that f∈A and x∈dom f.In the sequel C denotes aﬁnite set.The following propositions are true:(10)For every set V and for everyﬁnite set C and for every element A ofFin(V˙→C)holds Involved A⊆V.(11)For every set V and for everyﬁnite set C and for every element A ofFin(V˙→C)such that A=∅holds Involved A=∅.(12)For every set V and for everyﬁnite set C and for every element A ofFin(V˙→C)holds Involved A isﬁnite.(13)For everyﬁnite set C and for every element A of Fin(∅˙→C)holdsInvolved A=∅.Let V be a set,let C be aﬁnite set,and let A be an element of Fin(V˙→C).The functor−A yielding an element of Fin(V˙→C)is deﬁned as follows: (Def.2)−A={f;f ranges over elements of Involved A˙→C: g:element of V˙→C(g∈A⇒f≈g)}.One can prove the following propositions:(14)A −A=∅.(15)If A=∅,then−A={∅}.(16)If A={∅},then−A=∅.(17)For every set V and for everyﬁnite set C and for every element A ofSubstitutionSet(V,C)holdsµ(A −A)=⊥SubstLatt(V,C).(18)For every non empty set V and for everyﬁnite non empty set C and forevery element A of SubstitutionSet(V,C)such that A=∅holdsµ(−A)=⊤SubstLatt(V,C).lattice of substitutions is a heyting (325)(19)Let V be a set,C be aﬁnite set,A be an element ofSubstitutionSet(V,C),a be an element of V˙→C,and B be an elementof SubstitutionSet(V,C).Suppose B={a}.If A B=∅,then thereexists aﬁnite set b such that b∈−A and b⊆a.Let V be a set,let C be aﬁnite set,and let A,B be elements of Fin(V˙→C).The functor A֌B yielding an element of Fin(V˙→C)is deﬁned as follows: (Def.3)A֌B=(V˙→C)∩{ {f(i)\i;i ranges over elements of V˙→C: i∈A};f ranges over elements of A˙→B:dom f=A}.Next we state two propositions:(20)Let A,B be elements of Fin(V˙→C)and s be a set.Suppose s∈A֌B.Then there exists a partial function f from A to B such that s= {f(i)\i;i ranges over elements of V˙→C:i∈A}and dom f=A.(21)For every set V and for everyﬁnite set C and for every element A ofFin(V˙→C)such that A=∅holds A֌A={∅}.We adopt the following convention:u,v are elements of the carrier of SubstLatt(V,C),a is an element of V˙→C,and K,L are elements of SubstitutionSet(V,C).The following proposition is true(22)For every set X such that X⊆u holds X is an element of the carrier ofSubstLatt(V,C).ttice of Substitutions is ImplicativeLet us consider V,C.The functor pseudo compl(V,C)yielding a unary operation on the carrier of SubstLatt(V,C)is deﬁned as follows:(Def.4)For every element u′of SubstitutionSet(V,C)such that u′=u holds (pseudo compl(V,C))(u)=µ(−u′).The functor StrongImpl(V,C)yielding a binary operation on the carrier of SubstLatt(V,C)is deﬁned by:(Def.5)For all elements u′,v′of SubstitutionSet(V,C)such that u′=u and v′=v holds(StrongImpl(V,C))(u,v)=µ(u′֌v′).Let us consider u.The functor2u yielding an element of Fin(the carrier of SubstLatt(V,C))is deﬁned by:(Def.6)2u=2u.The functor \u yielding a unary operation on the carrier of SubstLatt(V,C) is deﬁned by:(Def.7)( \u )(v)=u\v.326adam grabowskiLet us consider V,C.The functor Atom(V,C)yielding a function from V˙→C into the carrier of SubstLatt(V,C)is deﬁned as follows:(Def.8)For every element a of V˙→C holds(Atom(V,C))(a)=µ{a}.Next we state a number of propositions:(23) f K Atom(V,C)=FinUnion(K,singleton V˙→C).(24)For every element u of SubstitutionSet(V,C)holds u= f u Atom(V,C).(25)( \u )(v)⊑u.(26)For every element a of V˙→C such that a isﬁnite and for every set csuch that c∈(Atom(V,C))(a)holds c=a.(27)For every element a of V˙→C such that K={a}and L=u and L K=∅holds(Atom(V,C))(a)⊑(pseudo compl(V,C))(u).(28)For everyﬁnite element a of V˙→C holds a∈(Atom(V,C))(a).(29)Let u,v be elements of SubstitutionSet(V,C).Suppose that for every setc such that c∈u there exists a set b such that b∈v and b⊆c∪a.Thenthere exists a set b such that b∈u֌v and b⊆a.(30)Let a be aﬁnite element of V˙→C.Suppose for every element b ofV˙→C such that b∈u holds b≈a and u⊓(Atom(V,C))(a)⊑v.Then(Atom(V,C))(a)⊑(StrongImpl(V,C))(u,v).(31)u⊓(pseudo compl(V,C))(u)=⊥SubstLatt(V,C).(32)u⊓(StrongImpl(V,C))(u,v)⊑v.Let us consider V,C.Observe that SubstLatt(V,C)is implicative.One can prove the following proposition(33)u⇒v= f2u((the meet operation of SubstLatt(V,C))◦(pseudo compl(V,C),(StrongImpl(V,C))◦( \u ,v))).References[1]Grzegorz Bancerek.Filters-part I.Formalized Mathematics,1(5):813–819,1990.[2]Czesław Byliński.Binary operations.Formalized Mathematics,1(1):175–180,1990.[3]Czesław Byliński.Functions and their basic properties.Formalized Mathematics,1(1):55–65,1990.[4]Czesław Byliński.Functions from a set to a set.Formalized Mathematics,1(1):153–164,1990.[5]Czesław Byliński.Partial functions.Formalized Mathematics,1(2):357–367,1990.[6]Czesław Byliński.Some basic properties of sets.Formalized Mathematics,1(1):47–53,1990.[7]Agata Darmochwał.Finite sets.Formalized Mathematics,1(1):165–167,1990.[8]Adam ttice of substitutions.Formalized Mathematics,6(3):359–361,1997.[9]Andrzej Trybulec.Binary operations applied to functions.Formalized Mathematics,1(2):329–334,1990.[10]Andrzej Trybulec.Finite join andﬁnite meet and dual lattices.Formalized Mathematics,1(5):983–988,1990.[11]Andrzej Trybulec.Semilattice operations onﬁnite subsets.Formalized Mathematics,1(2):369–376,1990.[12]Andrzej Trybulec.Tarski Grothendieck set theory.Formalized Mathematics,1(1):9–11,1990.lattice of substitutions is a heyting (327)[13]Andrzej Trybulec and Agata Darmochwał.Boolean domains.Formalized Mathematics,1(1):187–190,1990.[14]Zinaida Trybulec.Properties of subsets.Formalized Mathematics,1(1):67–71,1990.[15]Zinaida Trybulec and HalinaŚwięczkowska.Boolean properties of sets.Formalized Ma-thematics,1(1):17–23,1990.[16]Edmund Woronowicz.Relations and their basic properties.Formalized Mathematics,1(1):73–83,1990.[17]Edmund Woronowicz.Relations deﬁned on sets.Formalized Mathematics,1(1):181–186,1990.[18]StanisławŻukowski.Introduction to lattice theory.Formalized Mathematics,1(1):215–222,1990.Received December31,1998。

《语言学》Chapter 4 Syntax 习题兼答案

《新编简明英语语言学教程》第二版第4章练习题参考答案Chapter 4 Syntax1. What is syntax?Syntax is a branch of linguistics that studies how words are combined to form sentences and the rules that govern the formation of sentences.2. What is phrase structure rule?The grammatical mechanism that regulates the arrangement of elements (i.e. specifiers, heads, and complements) that make up a phrase is called a phrase structure rule.The phrase structural rule for NP, VP, AP, and PP can be written as follows:NP →(Det) N (PP) ...VP →(Qual) V (NP) ...AP →(Deg) A (PP) ...PP →(Deg) P (NP) ...We can formulate a single general phrasal structural rule in which X stands for the head N, V, A or P.3. What is category? How to determine a word's category?Category refers to a group of linguistic items which fulfill the same or similar functions in a particular language such as a sentence, a noun phrase or a verb.To determine a word's category, three criteria are usually employed, namely meaning, inflection and distribution.若详细回答，则要加上：Word categories often bear some relationship with its meaning. The meanings associated with nouns and verbs can be elaborated in various ways. The property or attribute of the entities denoted by nouns can be elaborated by adjectives. For example, when we say that pretty lady, we are attributing the property ‘pretty’ to the lady designated by the noun. Similarly, the properties and attributes of the actions, sensations and states designated by verbs can typically be denoted by adverbs. For example, in Jenny left quietly the adverb quietly indicates the manner of Jenny's leaving.The second criterion to determine a word's category is inflection. Words of different categories take different inflections. Such nouns as boy and desk take the plural affix -s. Verbs such as work and help take past tense affix -ed and progressive affix -ing. And adjectives like quiet and clever take comparative affix -er and superlative affix -est. Although inflection is very helpful in determining a word's category, it does not always suffice. Some words do not take inflections. For example, nouns like moisture, fog, do not usually take plural suffix -s and adjectives like frequent, intelligent do not take comparative and superlative affixes -er and -est.The last and more reliable criterion of determining a word's category is its distribution. That is what type of elements can co-occur with a certain word. For example, nouns can typically appear with a determiner like the girl and a card, verbs with an auxiliary such as should stay and will go, andadjectives with a degree word such as very cool and too bright.A word's distributional facts together with information about its meaning and inflectional capabilities help identify its syntactic category.4. What is coordinate structure and what properties does it have?The structure formed by joining two or more elements of the same type with the help of a conjunction is called coordinate structures.It has (或写Conjunction exhibits) four important properties:1) There is no limit on the number of coordinated categories that can appear prior to the conjunction.2) A category at any level (a head or an entire XP) can be coordinated.3) Coordinated categories must be of the same type.4) The category type of the coordinate phrase is identical to the category type of the elements beingconjoined.5. What elements does a phrase contain and what role does each element play?A phrase usually contains the following elements: head, specifier and complement. Sometimes it also contains another kind of element termed modifier.The role each element can play:Head:Head is the word around which a phrase is formed.Specifier:Specifier has both special semantic and syntactic roles. Semantically, it helps to make more precise the meaning of the head. Syntactically, it typically marks a phrase boundary.Complement:Complements are themselves phrases and provide information about entities and locations whose existence is implied by the meaning of the head.Modifier:Modifiers specify optionally expressible properties of the heads.6. What is deep structure and what is surface structure?There are two levels of syntactic structure. The first, formed by the XP rule in accordance with the head's subcategorization properties, is called deep structure(or D-structure). The second, corresponding to the final syntactic form of the sentence which results from appropriate transformations, is called surface structure (or S-structure).（以下几题只作初步的的成分划分，未画树形图, 仅供参考）7. Indicate the category of each word in the following sentences.a) The old lady got off the bus carefully.Det A N V P Det N Advb) The car suddenly crashed onto the river bank.Det N Adv V P Det Nc) The blinding snowstorm might delay the opening of the schools.Det A N Aux V Det N P Det Nd) This cloth feels quite soft.Det N V Deg A8. The following phrases include a head, a complement, and a specifier. Draw the appropriatetree structure for each.a) rich in mineralsXP(AP) →head (rich) A + complement (in minerals) PPb) often read detective storiesXP(VP) →specifier (often) Qual +head (read) V +complement (detective stories) NPc) the argument against the proposalsXP(NP) →specifier (the) Det +head (argument) N +complement (against the proposals) PP d) already above the windowXP(VP) →specifier (already) Deg +head (above) P +complement (the window) NPd) The apple might hit the man.S →NP (The apple) + Infl (might) +VP (hit the man)e) He often reads detective stories.S →NP (He) +VP (often reads detective stories)9. The following sentences contain modifiers of various types. For each sentence, first identify the modifier(s), then draw the tree structures.（斜体的为名词的修饰语，划底线的为动词的修饰语）a) A crippled passenger landed the airplane with extreme caution.b) A huge moon hung in the black sky.c) The man examined his car carefully yesterday.d) A wooden hut near the lake collapsed in the storm.10. The following sentences all contain conjoined categories. Draw a tree structure for each of the sentences.（划底线的为并列的范畴）a) Jim has washed the dirty shirts and pants.b) Helen put on her clothes and went out.c) Mary is fond of literature but tired of statistics.11. The following sentences all contain embedded clauses that function as complements of a verb, an adjective, a preposition or a noun. Draw a tree structure for each sentence.a) You know that I hate war.b) Gerry believes the fact that Anna flunked the English exam.c) Chris was happy that his father bought him a Rolls-Royce.d) The children argued over whether bats had wings.12. Each of the following sentences contains a relative clause. Draw the deep structure and the surface structure trees for each of these sentences.a) The essay that he wrote was excellent.b) Herbert bought a house that she lovedc) The girl whom he adores majors in linguistics.13. The derivations of the following sentences involve the inversion transformation. Give the deep structure and the surface structure of each of these sentences. （斜体的为深层结构，普通字体的为表层结构）a) Would you come tomorrow?you would come tomorrowb) What did Helen bring to the party?Helen brought what to the partyc) Who broke the window?who broke the window。

小学下册第十三次英语第四单元真题(含答案)

小学下册英语第四单元真题(含答案)考试时间：90分钟（总分:120）A卷一、综合题(共计100题共100分)1. 听力题：They are _____ (cooking/eating) dinner together.2. 听力题：Heat is a form of ______ energy.3. 填空题：The rabbit has a cute ______ (鼻子).4. 填空题：The ______ (小鸟) sits on a branch.5. 听力题：I have a _____ of chocolate in my bag. (bar)6. 选择题：What do we call the season when flowers bloom?A. AutumnB. WinterC. SpringD. Summer7. 选择题：What is the capital of Portugal?A. LisbonB. MadridC. RomeD. Athens答案: A. Lisbon8. 选择题：What do you call a group of fish swimming together?A. SchoolB. PackC. FlockD. Herd答案: A9. 填空题：I enjoy visiting the ________ (历史博物馆).10. 填空题：The ant builds complex ______ (巢穴) underground.11. 填空题：A ____(green marketing) emphasizes sustainability in advertising.12. 选择题：What is the name of the princess in "Aladdin"?A. JasmineB. ArielC. BelleD. Cinderella答案:A13. 选择题：What do we call the time when we eat lunch?A. BreakfastB. LunchC. DinnerD. Snack答案: B14. 听力题：A _______ is the state of matter that has a fixed volume but not a fixed shape.15. 听力题：The symbol for thorium is _____.16. 听力题：We collaborate on ________ (tasks) regularly.17. 选择题：What is the primary function of the heart?A. To digest foodB. To pump bloodC. To breatheD. To think答案: B18. 选择题：What is the capital of Venezuela?A. CaracasB. BogotaC. QuitoD. Lima19. 选择题：What is the primary color of a stop sign?a. Blueb. Yellowc. Redd. Green答案:C20. 选择题：What is the capital of Lesotho?a. Maserub. Teyateyanengc. Maputsoed. Mohale's Hoek答案:a21. 填空题：The ________ (植物适应性) to climate is amazing.22. 填空题：Elements on the left side of the periodic table are usually __________ (金属).23. 听力题：I will _____ (help/helped) you with your homework.24. 听力题：The chemical formula for sodium phosphate is _____.25. 填空题：I can ______ (参与) in community service projects.26. 选择题：What do we call the time when leaves fall from trees?A. SpringB. SummerC. FallD. Winter答案: C27. grant application) requests funding for initiatives. 填空题：The ____28. 选择题：What is the term for a young sheep?A. CalfB. FoalC. LambD. Kid答案:C29. 填空题：Violets are _______ flowers that bloom in spring.30. 选择题：根据短文内容,选出Tom和 Chen Jie 书包里的物品。

小学上册第十三次英语第2单元真题试卷(有答案)

小学上册英语第2单元真题试卷(有答案)英语试题一、综合题(本题有100小题，每小题1分，共100分.每小题不选、错误，均不给分)1.The __________ (人类历史) is full of incredible stories.2.I have _____ (one/two) pet cats.3.My cousin is very good at ____ (science).4.What do you call a person who studies ancient civilizations?A. HistorianB. ArchaeologistC. GeographerD. Anthropologist答案:B5.The _______ of a magnet can be demonstrated with iron filings.6.Did you see the _____ (兔子) hopping around?7.I want to ___ my room. (clean)8.Metals are typically ______ conductors of heat.9.We are ___ to school. (walking)10.__________ are important for the ecosystem because they pollinate flowers.11.Which bird is known for its colorful feathers and ability to mimic sounds?A. SparrowB. ParrotC. EagleD. Owl答案: B12.The ________ comes in many shapes and sizes.13. A __________ is a geological feature that can attract tourists.14.The dog is ________ in the park.15.We visit the ______ (艺术家工作室) to see creations.16. A cat's whiskers help it sense ______ (环境).17. A _______ is a tool that can help to measure the pressure of gases.18.The chemical formula for sulfuric acid is ______.19.Matter can exist in different states, including solid, liquid, and ________.20.Newton's laws describe the relationship between _______ and motion.21.What is the capital of Comoros?A. MoroniB. MoutsamoudouC. DomoniD. Mitsamiouli答案: A22.What do we call the liquid that falls from the sky?A. SnowB. RainC. HailD. Sleet答案:B.Rain23.What is the name of the famous painting of a woman with a mysterious smile?A. Starry NightB. The ScreamC. Mona LisaD. The Last Supper答案:C.Mona Lisa24.The ________ (人工栽培) supports agriculture.25.They are going to ________ a movie.26.My favorite subject in school is ______.27.The chemical formula for iron (II) sulfate is _______.28.I have a ________ (拼图游戏) of famous buildings.29.flora) of a region consists of its plant life. The ____30.What do we call the force that pulls objects toward each other?A. FrictionB. GravityC. MagnetismD. Inertia答案:B31.What is the name of the fairy that helps Peter Pan?A. Tinker BellB. CinderellaC. BelleD. Ariel答案: A32.Which planet do we live on?A. MarsB. EarthC. JupiterD. Saturn答案:B33.I like to eat ________ for breakfast.34.The __________ is known for its significant wildlife population. (非洲)35.I am excited to join the school ________ (合唱团) and sing with my friends.36.The pig loves to play in the ______.37.My friend loves __________ (户外活动).38.My teacher gives us ______ (作业) to help us learn new things. I try to finish it as soon as possible.39. A __________ is a natural feature formed by erosion.40.My uncle is a fantastic ____ (storyteller).41.__________ are substances that can donate protons in a reaction.42.What do you call the main part of a plant that supports it?A. RootB. StemC. LeafD. Flower答案:B43.The __________ is known for its vibrant nightlife.44.We should plant more ______ (树木).45. A shooting star is actually a ______ entering the Earth's atmosphere.46.Chemical reactions can be affected by _____, concentration, and surface area.47.It’s fun to build a ______ (雪堡) in the snow.48.What is the time when the sun sets called?A. DawnB. NoonC. DuskD. Midnight答案: C49.What is 60 ÷ 3?A. 15B. 20C. 25D. 30答案:b50.What is the name of the famous ancient city in Syria?A. PalmyraB. AleppoC. DamascusD. Homs答案:A.Palmyra51. A ______ (湿润的气候) supports lush vegetation.52.The _______ (小飞鱼) jumps out of the water to escape predators.53.We have a ______ (丰富的) menu for lunch.54.The ancient Romans used _____ to build their structures.55.I find joy in small ______ (事物) like a sunny day or a nice cup of hot chocolate. Life is full of little pleasures.56.The city of Helsinki is the capital of _______.57.I can ______ (提升) my creativity through art.58. A rainbow appears when light passes through _______.59.In spring, the _____ blooms beautifully.60.The wolf howls at the ________________ (月亮).61.What do we call the outer layer of the Earth?A. CoreB. MantleC. CrustD. Inner core答案:C62.The first person to receive a Nobel Prize was ______ (居里夫人).63.I like to watch _____ on TV. (cartoons)64.The ability of a solution to resist changes in pH is known as _____.65. A _______ can be used to measure the intensity of light.66.My sister enjoys practicing ____ (martial arts).67.What is the capital of Afghanistan?A. KabulB. KandaharC. HeratD. Mazar-i-Sharif答案: A68.The __________ is a large area of deep water.69. A rabbit's ears help it detect ______ (危险).70.The process of changing from liquid to gas is called ______.71.What do we call a person who repairs cars?A. MechanicB. DriverC. PilotD. Engineer答案:A72.Creating a ______ (家庭花园) can yield fresh produce.73. A _______ helps to measure the amount of pressure exerted on a surface.74.The ancient Greeks developed ________ to teach philosophy.75.What is the name of the famous scientist who proposed the theory of evolution?A. Isaac NewtonB. Albert EinsteinC. Charles DarwinD. Louis Pasteur答案:C76.sustainability report) evaluates progress. The ____77.I love to cook ______ (美味的食物) for my family. It’s a way to show my love and care.78.The Milky Way galaxy is a barred spiral _______.79.They are ___ a movie. (watching)80.What do we call a story that is made up?A. NonfictionB. BiographyC. FictionD. History答案: C81.The ______ (植物的演变) is an important topic in biology.82. A ______ (花园) can be a great hobby.83.What is the name of the famous Italian city known for its canals?A. VeniceB. RomeC. FlorenceD. Milan答案:A84.Which animal is known for its speed?A. TortoiseB. CheetahC. ElephantD. Sloth答案:B.Cheetah85.The _______ (The Scientific Method) transformed science and experimentation.86. A diatomic molecule consists of ______ atoms.87. A __________ is a landform created by the deposition of sediment.88.What is the capital of Barbados?A. BridgetownB. NassauC. KingstonD. Port au Prince答案: A89.The process of a liquid turning into gas is called _______.90.The first modern Olympics were held in ________ (1896).91.The __________ is a famous landmark in the United States. (自由女神像)92. A bison is a large, grazing ________________ (动物).93.My friend is always the first to __________ (帮助) others.94.My ________ (表哥) is studying hard for his exams.95.The chemical formula for potassium nitrate is ______.96.I saw a _______ (蝴蝶) land on a flower.97.The ____ has a shiny shell and is often found in gardens.98.The _______ of a battery is measured in volts.99.My sister is a good __________. (学生)100.What do we call a baby llama?A. CriaB. KidC. CalfD. Foal答案: A。

Unit,24年小学六年级上册第6次英语第四单元期中试卷

Unit,24年小学六年级上册英语第四单元期中试卷考试时间：90分钟（总分:110）B卷一、综合题(共计100题共100分)1. 听力题：A chemical that promotes combustion is called an ______.2. 选择题：What do you call the part of the day when the sun rises?A. MorningB. EveningC. AfternoonD. Night3. 填空题：I want to learn how to ________ (骑自行车).4. 选择题：What is the opposite of fast?A. QuickB. SlowC. SpeedyD. Rapid5. 选择题：What is the name of the famous ancient city in Egypt?A. CairoB. AlexandriaC. ThebesD. All of the above6. 填空题：The ________ (海岸线) is long and sandy.7. 选择题：What do you call the process of a seed growing into a plant?A. GerminationB. FertilizationC. PollinationD. Photosynthesis答案: A8. 选择题：What is the largest planet in our solar system?A. EarthB. MarsC. JupiterD. Venus9. 听力题：A _____ is a small celestial body that orbits the sun.10. 选择题：Which animal says "meow"?A. DogB. CatC. CowD. Sheep11. 听力题：The baby is _____ on the floor. (crawling)12. 填空题：My sister has a __________ (可爱的) smile.13. 听力题：I have a ___ (project/test) next week.14. 听力题：The pizza is ___ (delicious/yummy).15. 填空题：The _____ (根) helps to anchor the plant in the soil.16. 填空题：The dog barks _______ (很大声).17. 选择题：What do we call the act of telling someone to be quiet?A. SilenceB. HushC. ShhD. Quiet答案:B18. 填空题：__________ (表面张力) affects how liquids behave in different environments.19. 填空题：The _______ (The New Deal) introduced various programs to combat economic hardship.20. 听力题：An object that spins will continue to ______ (spin) unless acted upon by a force.21. 填空题：My aunt works as a __________ (护士) in the clinic.22. 填空题：The ancient Romans utilized ________ to enhance their architecture.23. 选择题：Which fruit is yellow?A. AppleB. BananaC. CherryD. Grape答案: B24. 选择题：What is the capital city of Samoa?A. ApiaB. Pago PagoC. MulifanuaD. Lalomanu25. 选择题：What do we call the main character in a story?A. AntagonistB. ProtagonistC. Supporting characterD. Minor character答案:B26. 选择题：What do you call a person who makes movies?A. DirectorB. ProducerC. ActorD. Filmmaker27. 填空题：My favorite holiday is ________ (万圣节) for the costumes.28. 填空题：I enjoy doing ______ (实验) in science class. It helps me learn through hands-on activities.29. 填空题：My dog has a very ______ (友好的) personality.30. 选择题：What do you call the act of doing something useful for someone else?A. HelpingB. AssistingC. ServingD. Supporting答案: A31. 选择题：How many months are there in a year?A. 10B. 12C. 11D. 932. 填空题：Brazil is famous for its _____ (47) during Carnival.33. 选择题：What is the opposite of "love"?A. HateB. LikeC. CareD. Enjoy34. 填空题：The ________ (农业实践改进) ensures sustainability.35. 听力题：The antelope is quick and agile in the ____.What do we call a person who catches fish?A. FishermanB. HunterC. FarmerD. Forager37. 选择题：What is the name of the famous mountain range in South America?A. RockiesB. AndesC. HimalayasD. Alps答案:B38. 填空题：The _____ (大自然) provides many resources.39. 听力题：A base turns red litmus paper ______.40. 选择题：Which animal is known for its ability to change colors?A. ChameleonB. FrogC. SnakeD. Fish答案: A41. 填空题：I love to ______ (与朋友分享) my interests.42. 选择题：What is the capital city of Angola?A. LuandaB. BenguelaC. HuamboD. Lubango43. 听力题：Chemical kinetics studies the rates of ______ reactions.44. 听力题：The process of ______ occurs when minerals crystallize.What do you call a small, flying insect that makes honey?A. BeeB. FlyC. MosquitoD. Ant答案:A46. 听力题：The process of changing from a gas to a liquid is called _______.47. 选择题：What is the largest mammal in the world?A. ElephantB. Blue WhaleC. GiraffeD. Hippo答案:B48. 听力题：The __________ is the process of a liquid turning into a solid.49. 选择题：What do we call the soft tissue inside bones?A. CartilageB. MarrowC. TendonD. Ligament答案:B50. 听力题：The chemical formula for brassylic acid is ______.51. 填空题：The __________ is known for its ancient temples and pyramids. (埃及)52. 填空题：A _______ (海马) swims in the sea.53. 听力题：The ____ is a small insect that can be found in many gardens.54. 听力题：The sandwiches are ___ (fresh/old).What is the term for the amount of space an object occupies?A. MassB. VolumeC. WeightD. Density答案:B56. 填空题：The ________ (地壳) is constantly changing.57. 填空题：I hope to make a positive impact on my _______ (社区). Every little effort counts.58. 听力题：A _______ is a solution that cannot dissolve any more solute.59. 选择题：What is the name of the famous American holiday celebrated on the fourth Thursday in November?A. ThanksgivingB. ChristmasC. New Year'sD. Independence Day答案:A60. 填空题：A _____ (盆栽) can add charm to any room.61. 填空题：In PE class, we play many sports like ________ (篮球) and ________ (排球). It helps us stay ________ (健康).62. 填空题：I enjoy going to the ______ (博物馆) to learn about science and history.63. 选择题：What do we call the time it takes for the Earth to rotate once on its axis?A. YearB. MonthC. DayD. Hour答案:C. DayWhich animal is known for its long neck?A. ElephantB. GiraffeC. HorseD. Dog答案:B65. 听力题：The cat likes to _____ in the sun. (nap)66. 填空题：The ______ (植物的医用特性) are explored in research.67. 选择题：What is the opposite of "happy"?A. JoyfulB. SadC. ExcitedD. Angry答案:B68. 选择题：What is 20 15?A. 4B. 5C. 6D. 769. 听力题：The teacher is very ________.70. 听力题：The process of ______ can lead to the formation of new landforms.71. 选择题：What do you call the middle of the Earth?A. CrustB. MantleC. CoreD. Shell答案: C72. 听力题：The _____ (钱包) is on the table.What is the name of the famous lighthouse in Greece?A. Pharos of AlexandriaB. Cape HatterasC. Eddystone LighthouseD. Portland Head Lighthouse74. 听力题：Turtles have a hard ______ for protection.75. 选择题：Which of these is a popular sport?A. ChessB. FencingC. FootballD. Knitting76. 听力题：They like _____ (to run) in the park.77. 填空题：My friend, ______ (我的朋友), has a pet rabbit.78. 听力题：She has a red ___. (bike)79. 选择题：What do we call a young alligator?A. HatchlingB. PupC. KitD. Chick答案:A. Hatchling80. 填空题：I can ______ (跑) fast.81. 填空题：Playing with toys helps me learn how to ________ (动词) with others. It teaches me important ________ (名词).82. 听力题：A chemical change can result in a change in ______.83. 选择题：What is the term for a plant that grows in dry conditions?A. AquaticB. TerrestrialC. XerophyticD. Epiphytic答案:C84. 选择题：What is the name of the famous ancient city in Peru?A. Machu PicchuB. CuscoC. LimaD. Arequipa答案:A85. 填空题：We have _______ for breakfast.86. 听力题：The girl loves to ________.87. 选择题：What is the name of the famous archaeological site in Italy?A. PompeiiB. HerculaneumC. Ostia AnticaD. All of the above答案: D. All of the above88. 填空题：My favorite _____ (玩具小汽车) is red.89. 填空题：Planting trees can help combat ______ (气候变化).90. 听力题：The Earth's surface is influenced by both climatic and ______ factors.91. 填空题：The _____ (野生)flowers bloom in springtime.92. 选择题：What do you call a solid that has no definite shape?A. LiquidB. GasC. SolidD. Plasma答案:A93. 听力题：I like to ride my ______ (bike) after school.94. 填空题：The _______ (The Treaty of Versailles) ended World War I and imposed penalties on Germany.95. 选择题：What do you call a baby cow?A. CalfB. FoalC. KidD. Lamb答案:A96. 填空题：The country known for its tea ceremonies is ________ (日本).97. 听力题：The __________ can indicate areas at risk of environmental degradation.98. 听力题：The _______ of an object can be changed by adding or removing mass.99. n Wall fell in _____. 填空题：The Berl100. 听力题：An emulsion is a mixture of two liquids that do not _____.。

小学上册第十四次英语第6单元真题[含答案]

小学上册英语第6单元真题[含答案]英语试题一、综合题(本题有100小题，每小题1分，共100分.每小题不选、错误，均不给分)1.The __________ (人际关系) are important for happiness.2.What do we call a scientist who studies the atmosphere?A. MeteorologistB. ClimatologistC. Environmental ScientistD. Geochemist3.The Earth's crust is divided into large sections called ______ plates.4.They are going to a ________.5. A ____(land use) survey assesses how land is used.6.My aunt is a ______. She loves to teach children.7.The ______ (温室) helps plants grow in winter.8.The ________ is a famous desert in Africa.9.I like to go ______ (远足) to enjoy the beauty of nature.10.Which animal is known as the king of the jungle?A. TigerB. LionC. BearD. Elephant11._____ (pruning) helps plants grow better.12.The __________ (树) grows tall and strong in the forest.13. A ______ (园丁) enjoys working with soil.14.Which of these is a winter sport?A. SoccerB. SwimmingC. SkiingD. Basketball答案:C15. A _____ (bouquet) of flowers makes a lovely gift.16. A __________ (色素) gives color to plants and flowers.17.My sister has a pet ______ (鹦鹉) that talks.18.plate tectonics) theory explains earthquakes. The ____19.The ________ (乡村) is peaceful and quiet.20.The ______ (狼) howls at the moon.21.The process of fermentation converts sugar into ______.22. A displacement reaction involves one element replacing ______.23.The process of distillation separates liquids based on their _____.24.My dog likes to dig in the ______ (沙子).25.What is the color of a typical blueberry?A. GreenB. BlueC. RedD. Purple答案:B26.My brother is a ______. He enjoys drawing.27.I enjoy watching the ______ (日出) in the morning.28.The chemical formula for cyclopentane is ______.29.Which animal is known for its wisdom?A. OwlB. EagleC. ParrotD. Crow答案:A30.Neutrons have no ______ charge.31.What is the largest mammal in the world?A. ElephantB. Blue WhaleC. GiraffeD. Hippopotamus答案:B32.I like to ______ (参加) workshops.33.My cousin is a ______. She enjoys traveling to new countries.34.The ______ (小鱼) swims gracefully through the coral reef.35.What do you call a young squirrel?A. KitB. PupC. KittenD. Baby36.The atomic number of an element is determined by the number of ______ it has.37. A ____(sustainable city) prioritizes balance between nature and urban life.38.What sound does a cow make?A. MeowB. BarkC. MooD. Quack39.I want to ________ (learn) a new language.40.I enjoy writing letters to my _______ (朋友) who live far away. It keeps our friendship strong.41.The ancient Greeks are famous for their _______ and philosophy.42.The sky is _______ (阴暗的) today.43.The jackal is a clever ______ (动物).44._______ can grow in both sunny and shady places.45.Which of these is a basic shape?A. CircleB. OctagonC. HexagonD. Rhombus46.The chemical formula for sodium sulfate is ______.47.The ______ (田野) is full of blooming flowers.48.The girl sings very ________.49.What do you call the food that comes from cows?A. BreadB. CheeseC. ChickenD. Fish答案:B50.What do we call a set of instructions for a computer?A. ProgramB. SoftwareC. ApplicationD. Code答案:D51.The chemical formula for iodine monochloride is _______.52.The owl can turn its head almost _______ (完全) around.53.The anteater has a long ________________ (舌头).54. A ______ is a type of reaction that involves heat.55.What is the capital of Finland?A. TallinnB. OsloC. HelsinkiD. Stockholm答案:C Helsinki56.My grandfather tells me interesting ________ (故事) about his childhood. I listen carefully and ask him many ________ (问题).57.What is the name of the famous tower in Paris?A. Leaning Tower of PisaB. Burj KhalifaC. Eiffel TowerD. Empire State Building答案:C58.My cat loves to play with _______ (毛线).59.The __________ was so bright that I had to wear sunglasses. (阳光)60.The ______ (海龟) lays eggs on sandy beaches.61.What is the name of the plant that is known for its medicinal properties?A. FernB. Aloe VeraC. CactusD. Moss答案:B62.The dog is _____ (barking/sleeping) in the yard.63.The butterfly emerges from its _____ chrysalis.64.I want to learn to _____ (swim/fly).65.ts can grow from __________ (切割). Some pla66.After school, I play video games with my ________ (朋友) online. It’s so much ________ (乐趣).67.The butterfly starts as a ______.68.The process of oxidation involves __________ losing electrons.69.I can ______ (清楚地表达) my ideas.70.The ant is very _______ (团结) with its colony.71.The clock shows _____ (ten/twelve).72. A compound is formed when two or more different ______ combine.73.The ________ (地理学) is fascinating to study.74.How many players are on a polo team?A. 4B. 5C. 6D. 775.My favorite color is ______ (red).76.What is the opposite of 'big'?A. HugeB. SmallC. TallD. Large77.What is the capital of Iceland?A. ReykjavikB. AkureyriC. SelfossD. Keflavik答案:A78. A rabbit’s teeth are always ______ (生长).79.The wind is _______ (blowing) through the trees.80.The penguin waddles on ________________ (冰).81.What is the name of the famous clock tower in London?A. Big BenB. Eiffel TowerC. Leaning Tower of PisaD. Burj Khalifa82.The eagle flies high in the _________. (天空)83.Which fruit is yellow?A. AppleB. BananaC. CherryD. Grape答案:B84.The __________ (海洋生物) are fascinating to study.85.He _____ (plays/played) video games all day.86.We have a ______ (特别的) event this weekend.87.The octopus has three ______ (心脏).88.I can _____ (跳舞) well.89.The owl is active at ______.90. A strong acid can corrode ______ materials.91.I like _____ (旅行) with my family.92.What do you call a person who makes bread?A. BakerB. ChefC. CookD. Caterer答案:A93.The __________ (大西洋奴隶贸易) was a dark part of history.94. A diatomic molecule consists of two atoms of the _____ element.95.Which season is known for blooming flowers?A. WinterB. SpringC. SummerD. Fall答案:B96. A chemical reaction that releases light is called a _______ reaction.97.The ____ is a friendly animal that loves to be petted.98.What is the name of the famous artist known for his sculptures?A. MichelangeloB. RembrandtC. Van GoghD. Renoir答案:A99.What is the capital of Greece?A. AthensB. ThessalonikiC. CreteD. Rhodes100.What is the name of the famous detective created by Arthur Conan Doyle?A. Sherlock HolmesB. Hercule PoirotC. Miss MarpleD. Sam Spade。

西安“PEP”2024年小学六年级第8次英语第一单元期中试卷

西安“PEP”2024年小学六年级英语第一单元期中试卷考试时间：100分钟（总分:120）B卷一、综合题(共计100题共100分)1. 选择题：Which of these is a type of fish?A. SalmonB. ChickenC. PorkD. Beef答案:A2. 填空题：The __________ (历史的交汇) creates possibilities.3. 填空题：The ________ likes to swim in the pool.4. 选择题：How many days are in a leap year?A. 365B. 366C. 367D. 364答案:B5. 听力题：A ______ is a homogeneous mixture of two or more substances.6. 填空题：My mom grows ________ in the kitchen.7. 听力题：A __________ is a piece of land surrounded by water on all sides.8. 填空题：Vines can _____ (攀爬) up walls.9. 听力题：The chemical formula for calcium carbonate is ______.10. 填空题：The ________ is a significant structure in London.11. 选择题：What do you call the person who writes a book?A. ReaderB. AuthorC. EditorD. Publisher答案: B. Author12. 填空题：The __________ (历史的反馈) influences future research.13. 选择题：What do you call a story about a person's experiences?A. NarrativeB. BiographyC. AutobiographyD. All of the above答案:D14. 听力题：My uncle loves collecting ____ (comic books).15. 填空题：My uncle is a __________ (电工).16. 听力题：The _______ changes with the seasons.17. 填空题：We celebrate my brother’s __________ every year. (生日)18. 填空题：The cat's purring is a sign of ______ (放松).19. 选择题：What do you call the process of making bread rise?A. FermentationB. ProofingC. KneadingD. Mixing20. 填空题：I love to play ______ outside.21. 听力题：__________ are substances that can conduct electricity when dissolved in water.22. 听力题：The __________ can provide critical insights into the impacts of climate change.23. 听力题：The capital of Georgia is __________.24. 听力题：The chemical symbol for silver is ______.25. 听力题：The caterpillar turns into a _____.26. 填空题：The first human to break the sound barrier was ______ (查尔斯·扬)。

小学下册第13次英语第3单元真题(有答案)

小学下册英语第3单元真题(有答案)英语试题一、综合题(本题有100小题，每小题1分，共100分.每小题不选、错误，均不给分)1.The chemical formula for glucose is _______.2. A _______ is a type of reaction that breaks down compounds into simpler substances.3.What is the value of 10 5 + 3?A. 5B. 6C. 7D. 8答案:B4.We will _______ (make) cookies this afternoon.5.The __________ (植物的生命周期) is fascinating to observe.6. A ________ (热带雨林) is rich in biodiversity.7.We are going to the ___. (planetarium)8.The ____ is a tiny animal that loves to hop around in gardens.9.My cousin has a __________ cat. (可爱的)10. A __________ is a geological feature that provides habitats for wildlife.11. A pulley can help lift heavy ______.12.The _______ of light can be affected by the angle of incidence.13.Which insect can make honey?A. AntB. ButterflyC. BeeD. Fly答案:C14.What kind of animal is an octopus?A. MammalB. FishC. ReptileD. Mollusk答案: D15. A polymer is a large molecule made of many ______.16.What is the name of the river that flows through Egypt?A. AmazonB. NileC. YangtzeD. Mississippi答案:B.Nile17.My dad, ______ (我爸爸), loves to tell jokes.18.The __________ is the area where fresh water meets salt water.19.Plants need ______ (水) to survive and grow.20.In _____ (美国), the Grand Canyon is a popular destination.21.I enjoy drawing ______ in my spare time.22.The ______ is a common pet that barks.23.The __________ (植物的生理) is fascinating to study.24.The antelope runs swiftly from danger in the ____.25.Listen and tick.听录音，在正确图片下的字母上打“√”。

英语修辞手法课件高考英语专题复习

英语修辞手法 English rhetoric
Simile 明喻
• 明喻是将具有共性的不同事物作对比.这种共性存在于人们的心里,而不是事物的自然属性.
• 标志词常用 like, as, seem, as if, as though, similar to, such as 等.
• 例如: • 1）He was like a cock who thought the sun
• 提喻用部分代替全体,或用全体代替部分,或特殊代替一般.
例如: • 1）There are about 100 hands working in his
factory.(部分代整体) 他的厂里约有 100 名工人. • 2）He is the Newton of this century.(特殊代一般) 他是本世纪的牛顿. • 3）The fox goes very well with your cap.（整体代部分）
Personification 拟人
• It gives human form of feelings to animals, or life and personal attributes(赋予) to inanimate(无生命的) objects, or to ideas and abstractions(抽象). 拟人（personification）
Allegory 讽喻,比方（原意“寓言”）
• 建立在假借过去或别处的事例与对象之上，传达暗示，影射或者讥讽现世各种现象的含义。
• 英文解释：an expressive style that uses fictional characters and events to describe somesubject by suggestive resemblances; an extended metaphor 摘自英语专业《大学英语教程》一书

沪教版英语小学五年级上学期期末试题及答案指导(2024-2025学年)

2024-2025学年沪教版英语小学五年级上学期期末模拟试题及答案指导一、听力部分（本大题有12小题，每小题2分，共24分）1、What is the name of the capital city in China?A. ShanghaiB. BeijingC. GuangzhouD. ShenzhenAnswer: BExplanation: The capital city of China is Beijing. The other options are major cities in China, but not the capital.2、How do you say “I have a cat” in English?A. I have a dogB. I have a catC. I have a birdD. I have a fishAnswer: BExplanation: The correct translation of “我有只猫” (Wo you zhi mao) into English is “I have a cat.” The other options are translations of differentanimals.3、Listen to the dialogue and choose the best answer for each question. (听对话，回答下列问题。

)3、How does Tom go to school today?A、By bus.B、By bike.C、On foot.3、C、On foot.解析: In the dialogue, Tom says, “I usually go to school on foot, but today I walked faster because I was in a hurry.” Therefore, the correct answer is C, “On foot.”4、What’s the weather like today?A、Sunny.B、Rainy.C、Cloudy.4、B、Rainy.解析: The dialogue mentions that “Tom’s father said, ‘It’s going to rain today, so make sure to bring an umbrella.’” Therefore, the correct answer is B, “Rainy.”5.Listen to the dialogue between two students about their weekend plans. Select the best answer to fill in the blank.Student A: Hey, do you know what you are doing this weekend?Student B: Well, I’m going to visit my grandparents in the countryside.Student A: That sounds nice. What about you?Student B: I’m planning to go to the lake with my friends to swim and enjoy the nature.Question: What is Student B’s plan for the weekend?A)Visiting a friend in the city.B)Playing video games at home.C)Traveling to the countryside to visit grandparents.D)Going to the lake with friends.Answer: C) Traveling to the countryside to visit grandparents.Explanation: The conversation between the students clearly indicates Student B’s plan to travel to the countryside to visit their grandparents.6.Listen to a short passage about different types of fruits. Answer the following question.Question: According to the passage, which of the following fruits is not mentioned?A)ApplesB)BananasC)CherriesD)GrapesE)OrangesAnswer: C) CherriesExplanation: The passage mentions apples, bananas, grapes, and oranges asdifferent types of fruits; Cherries are not mentioned in the list.7、Listen to the dialogue and choose the correct answer.A. How old is the boy?B. How many books does the girl have?C. What is the weather like today?Answer: BExplanation: The boy asks, “How many books do you have?” indicating that the topic of the conversation is about the number of books the girl has. The other options are not addressed in the dialogue.8、Listen to the following instructions and complete the sentence.You will hear a teacher giving instructions for a group activity. Listen carefully and fill in the blank.The teacher says, “For our next activity, you will be working in groups of _______.”Answer: 4Explanation: The teacher’s instruction implies that the students will be divided into groups of four. The blank needs to be filled with the number “4” to complete the sentence correctly.9、Question:Listen to the sentence and choose the correct answer.Sentence:A: What is your favorite subject?B: My favorite subject is math.Answer: CExplanation:In the conversation, B says that his favorite subject is math. Therefore, the correct answer is C.10、Question:Listen to the sentence and choose the correct answer.Sentence:A: How do you go to school?B: I usually go to school by bus.Answer: BExplanation:In the dialogue, B indicates that he usually goes to school by bus. Thus, the correct answer is B.11.Listen to the dialogue between two students discussing their weekend plans. Choose the correct answer to complete the sentence.A. They are going to the zoo on Saturday.B. They are planning a picnic on Sunday.C. They will visit their families.Answer: BExplanation: In the dialogue, the first student mentions that they are planning a picnic on Sunday, implying that they will gather food and spend time outdoors together.12.Listen to a short passage about the importance of reading books. After listening, answer the following question.How can reading books help a person?A. It makes them healthier.B. It encourages creativity.C. It improves mathematical skills.Answer: BExplanation: The passage emphasizes that reading books stimulates creativity, as it allows readers to imagine new worlds, characters, and situations, which in turn enhances their imagination and thinking abilities.二、选择题（本大题有12小题，每小题2分，共24分）1、Which of the following is a plural noun?A. CatB. DogC. BooksD. TreeAnswer: CExplanation: In English, a plural noun refers to more than one of a thing.Option C, “Books,” is the plural form of the word “Book,” indicating more than one book. Options A, B, and D are all singular nouns.2、What does “She is reading a book.” mean?A. She is writing a book.B. She is looking at a book but not reading it.C. She is reading the contents of a book.D. She is borrowing a book.Answer: CExplanation: The sentence “She is reading a book” means that she is actively engaging with the contents of a book by reading it. Option A refers to writing a book, which is different from reading. Option B suggests merely looking at a book without reading, which does not convey the same meaning. Option D refers to borrowing a book, which is also unrelated to the action of reading. Therefore, the correct answer is C.3、Which sentence is correct?A)She go to school by bus every day.B)She goes to school by bus every day.C)She going to school by bus every day.D)She went to school by bus every day.Answer: BExplanation: The correct choice is B because it uses the proper verb form ‘goes’ which agrees with the singular subject ‘She’. Option A incorrectly uses the base form of the verb ‘go’, while C incorrectly uses the presentparticiple ‘going’ without a main verb. Option D is in the past tense, which does not fit the context of an ongoing action described by ‘every day’.4、What should you say when someone gives you a gift?A)You’re welcome.B)Thank you very much.C)I don’t like it.D)It’s none of your business.Answer: BExplanation: The correct choice is B. When receiving a gift, it is polite to express gratitude by saying ‘Thank you very much.’ Option A is used to respond to thanks, not to give them. Options C and D are impolite and would be inappropriate responses when given a gift.5.Choose the correct word to complete the sentence.Tom is a good student. He always keeps his classroom __________.A. cleanB. clearC. clearnessD. clearableAnswer: AExplanation: The correct word to complete the sentence is “clean” becau se it means to be free from dirt or disorder, which is the expected behavior ofa good student in keeping his classroom.6.Select the sentence that has the correct subject-verb agreement.A. The students are playing football.B. The students is playing football.C. The students be playing football.D. The students playing football.Answer: AExplanation: The correct sentence is “The students are playing football” because the subject “the students” is plural, so the verb “are” should be used to agree with the subject in number. The other options have incorrect verb conjugation or agreement.7、Which day of the week comes after Wednesday?A)MondayB)TuesdayC)ThursdayAnswer: C) ThursdayExplanation: The days of the week in order are Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, and Sunday. Therefore, Thursday comes after Wednesday.8、What is the result of 45 ÷ 9?A)4B)5C)6Answer: B) 5Explanation: To find the result of 45 ÷ 9, divi de 45 by 9.45 ÷ 9 = 59.What is the plural form of the word “cat”?A)catB)catsC)cat’sAnswer: B) catsExplanation: The word “cat” is a singular noun. Its plural form is “cats.”10.Choose the correct verb form to complete the sentence.Yesterday, Emily___________her homework.A)finishedB)finishesC)is finishingAnswer: A) finishedExplanation: The sentence talks about an action that Emily did yesterday, which is in the past. Therefore, the correct form to use is the past simple tense, “finished.”11、What day is it tomorrow?A. MondayB. TuesdayC. WednesdayD. ThursdayAnswer: AExplanation: The context or previous information in the test paper should indicate or imply that today is Sunday, making tomorrow Monday. Without direct context here, the answer is based on typical test logic where options are distinct and not overlapping in a direct sequence question.12、—— How_____is your brother?—— He is 1.65 meters.A. oldB. tallC. heavyD. longAnswer: BExplanation: The response “He is 1.65 meters” indicates a measurement of height. Therefore, the correct question to ask would be about how tall someone is. “Old” refers to age, “heavy” refers to weight, and “long” is generally not used to describe a person’s height in this context.三、完型填空（10分）Section III: Cloze TestDirections: Read the passage carefully. Then fill in each blank with the correct form of the word given in brackets.Passage:Tommy is a 1 (five) grade student. He usually goes to school by bus, buttoday he went by bike because the bus was late. After school, he met his friend Jerry near the school gate. They decided to go to the park to play football. When they got there, they saw many children playing games. Tommy and Jerry joined them and had a lot of 2(funny). After playing, they were very thirsty, so they went to buy some drinks. On their way back home, they found a little dog lying on the street. It looked lost and hungry. Tommy and Jerry took it to an animal shelter nearby. The workers there said they would take good care of the dog. Tommy and Jerry felt happy that they could help the little dog. At last, they went home and told their parents about their day. Their parents were proud of them for being so 3 (kind).Questions:1.Tommy is a 1 (five) grade student.2.They decided to go to the park to play football and had a lot of 2(funny).3.Their parents were proud of them for being so 3 (kind).Answer Key:1.fifth2.fun3.kindThis cloze test aims to assess the students’ understanding of basic vocabulary, such as numbers and adjectives, as well as their ability to use words correctly in context. It also includes a simple narrative to encourage reading comprehension.四、阅读理解（26分）Reading ComprehensionRead the following passage and answer the questions that follow.The Shanghai Zoo, located in the heart of Shanghai, is one of the most popular tourist attractions in the city. With over 1,200 animals from around the world, the zoo offers a unique opportunity for visitors to learn about wildlife and conservation. The zoo covers an area of 220 hectares and is divided into several sections, each focusing on a different part of the animal kingdom.One of the most interesting sections of the zoo is the Primate House. Here, visitors can observe various species of monkeys, such as the Macaque and the Rhesus macaque. These primates are known for their intelligence and social behavior. Another highlight is the Elephants and Lions section, where you can see these majestic creatures up close. The zoo also has a special section for endangered animals, where visitors can learn about conservation efforts and the importance of protecting wildlife.Question 1: What is the main purpose of the Shanghai Zoo?A. To provide entertainment for visitors.B. To educate people about wildlife and conservation.C. To sell animals to tourists.D. To offer a place for people to exercise.Question 2: How many hectares does the Shanghai Zoo cover?A. 50 hectaresB. 100 hectaresC. 220 hectaresD. 500 hectaresQuestion 3: Which section of the zoo is known for housing intelligent primates?A. The Elephants and Lions sectionB. The Endangered Animals sectionC. The Primate HouseD. The Birds sectionAnswer Key:1.B. To educate people about wildlife and conservation.2.C. 220 hectares3.C. The Primate House五、写作题（16分）Section Five: Writing (Writing)Instructions:Write a short passage about your favorite book. Include the title, the author, why you enjoy it, and any memorable scenes or characters. Your passage should be at least 50 words.Example:My favorite book is “Charlotte’s Web” by E.B. White. This book tells the storyof a little girl named Fern, who saves her pet pig, Wilbur, from being sold to a slaughterhouse. Wilbur becomes a pig for a fair, and Charlotte, a friendly spider living on the farm, becomes his friend. They both become great friends, and Charlotte helps Wilbur win a prize at the fair by writing wonderful words in her web. I love this book because it shows that true friendship is more important than material things. Especially, the story of the spider and the pig is so heart-warming and touching.Analysis:•Content: Ensure the passage includes the title, author, and personal reasons for enjoying the book, along with memorable scenes or characters.•Structure: The example is organized clearly into sections about the book’s content, the author, and th e personal connection to the story.•Vocabulary & Grammar: The example uses appropriate vocabulary for a Grade5 student, along with proper grammar and sentence structure.•Length: The example meets the 50-word requirement, which helps students understand the minimum length necessary.•Cohesion: The writing shows a clear flow of ideas and maintains coherence throughout the passage.This writing task tests students’ ability to write a short, coherent passage based on a chosen book and to use appropriate language and content.。

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JOURNAL OF FORMALIZED MATHEMATICSVolume10,Released1998,Published2003Inst.of Computer Science,Univ.of BiałystokLattice of Substitutions is a Heyting AlgebraAdam GrabowskiUniversity of BiałystokMML Identiﬁer:HEYTING2.WWW:/JFM/Vol10/heyting2.htmlThe articles[11],[6],[14],[15],[3],[16],[9],[2],[7],[13],[4],[5],[17],[8],[10],[12],and[1] provide the notation and terminology for this paper.1.P RELIMINARIESWe follow the rules:V,C,x denote sets and A,B denote elements of SubstitutionSet(V,C).Let a,b be sets.Observe that{ a,b }is function-like and relation-like.One can prove the following propositions:(1)For all non empty sets V,C there exists an element f of V˙→C such that f=/0.(2)For all sets a,b such that b∈SubstitutionSet(V,C)and a∈b holds a is aﬁnite function.(3)For every element f of V˙→C and for every set g such that g⊆f holds g∈V˙→C.(4)V˙→C⊆2[:V,C:].(5)If V isﬁnite and C isﬁnite,then V˙→C isﬁnite.Let us observe that there exists a set which is functional,ﬁnite,and non empty.2.S OME P ROPERTIES OF S ETS OF S UBSTITUTIONSThe following four propositions are true:(6)For everyﬁnite element a of V˙→C holds{a}∈SubstitutionSet(V,C).(7)If A B=A,then for every set a such that a∈A there exists a set b such that b∈B andb⊆a.(8)Ifµ(A B)=A,then for every set a such that a∈A there exists a set b such that b∈B andb⊆a.(9)If for every set a such that a∈A there exists a set b such that b∈B and b⊆a,thenµ(A B)=A.Let V be a set,let C be aﬁnite set,and let A be an element of Fin(V˙→C).The functor Involved A is deﬁned by:(Def.1)x∈Involved A iff there exists aﬁnite function f such that f∈A and x∈dom f.1c Association of Mizar UsersIn the sequel C is aﬁnite set.One can prove the following propositions:(10)For every set V and for everyﬁnite set C and for every element A of Fin(V˙→C)holdsInvolved A⊆V.(11)For every set V and for everyﬁnite set C and for every element A of Fin(V˙→C)such thatA=/0holds Involved A=/0.(12)For every set V and for everyﬁnite set C and for every element A of Fin(V˙→C)holdsInvolved A isﬁnite.(13)For everyﬁnite set C and for every element A of Fin(/0˙→C)holds Involved A=/0.Let V be a set,let C be aﬁnite set,and let A be an element of Fin(V˙→C).The functor−A yields an element of Fin(V˙→C)and is deﬁned as follows:(Def.2)−A={f;f ranges over elements of Involved A˙→C:g:element of V˙→C(g∈A⇒f≈g)}.One can prove the following propositions:(14)A −A=/0.(15)If A=/0,then−A={/0}.(16)If A={/0},then−A=/0.(17)For every set V and for everyﬁnite set C and for every element A of SubstitutionSet(V,C)holdsµ(A −A)=⊥SubstLatt(V,C).(18)For every non empty set V and for everyﬁnite non empty set C and for every element A ofSubstitutionSet(V,C)such that A=/0holdsµ(−A)=⊤SubstLatt(V,C).(19)Let V be a set,C be aﬁnite set,A be an element of SubstitutionSet(V,C),a be an elementof V˙→C,and B be an element of SubstitutionSet(V,C).Suppose B={a}.If A B=/0,then there exists aﬁnite set b such that b∈−A and b⊆a.Let V be a set,let C be aﬁnite set,and let A,B be elements of Fin(V˙→C).The functor A֌B yields an element of Fin(V˙→C)and is deﬁned as follows:(Def.3)A֌B=(V˙→C)∩{{f(i)\i;i ranges over elements of V˙→C:i∈A};f ranges over elements of A˙→B:dom f=A}.The following two propositions are true:(20)Let A,B be elements of Fin(V˙→C)and s be a set.Suppose s∈A֌B.Then there existsa partial function f from A to B such that s={f(i)\i;i ranges over elements of V˙→C: i∈A}and dom f=A.(21)For every set V and for everyﬁnite set C and for every element A of Fin(V˙→C)such thatA=/0holds A֌A={/0}.We adopt the following rules:u,v are elements of SubstLatt(V,C),a is an element of V˙→C,and K,L are elements of SubstitutionSet(V,C).One can prove the following proposition(22)For every set X such that X⊆u holds X is an element of SubstLatt(V,C).3.L ATTICE OF S UBSTITUTIONS IS I MPLICATIVELet us consider V,C.The functor pseudocompl(V,C))(u)=µ(−u′).The functor StrongImpl(V,C)yields a binary operation on the carrier of SubstLatt(V,C)and isdeﬁned by:(Def.5)For all elements u′,v′of SubstitutionSet(V,C)such that u′=u and v′=v holds (StrongImpl(V,C))(u,v)=µ(u′֌v′).Let us consider u.The functor2u yielding an element of Fin(the carrier of SubstLatt(V,C))isdeﬁned by:(Def.6)2u=2u.The functor \u yielding a unary operation on the carrier of SubstLatt(V,C)is deﬁned as follows: (Def.7)( \u )(v)=u\v.Let us consider V,C.The functor Atom(V,C)yielding a function from V˙→C into the carrier of SubstLatt(V,C)is deﬁned by:(Def.8)For every element a of V˙→C holds(Atom(V,C))(a)=µ{a}.One can prove the following propositions:(23) fKAtom(V,C)=FinUnion(K,singleton V˙→C).(24)For every element u of SubstitutionSet(V,C)holds u= fuAtom(V,C).(25)( \u )(v)⊑u.(26)For every element a of V˙→C such that a isﬁnite and for every set c such that c∈(Atom(V,C))(a)holds c=a.(27)For every element a of V˙→C such that K={a}and L=u and L K=/0holds(Atom(V,C))(a)⊑(pseudocompl(V,C))(u)=⊥SubstLatt(V,C).(32)u⊓(StrongImpl(V,C))(u,v)⊑v.Let us consider V,C.Observe that SubstLatt(V,C)is implicative.Next we state the proposition(33)u⇒v= f2u((the meet operation of SubstLatt(V,C))◦(pseudoR EFERENCES[1]Grzegorz Bancerek.Filters—part I.Journal of Formalized Mathematics,2,1990./JFM/Vol2/filter_0.html.[2]Czesław Byli´n ski.Binary operations.Journal of Formalized Mathematics,1,1989./JFM/Vol1/binop_1.html.[3]Czesław Byli´n ski.Functions and their basic properties.Journal of Formalized Mathematics,1,1989./JFM/Vol1/funct_1.html.[4]Czesław Byli´n ski.Functions from a set to a set.Journal of Formalized Mathematics,1,1989./JFM/Vol1/funct_2.html.[5]Czesław Byli´n ski.Partial functions.Journal of Formalized Mathematics,1,1989./JFM/Vol1/partfun1.html.[6]Czesław Byli´n ski.Some basic properties of sets.Journal of Formalized Mathematics,1,1989./JFM/Vol1/zfmisc_1.html.[7]Agata Darmochwał.Finite sets.Journal of Formalized Mathematics,1,1989./JFM/Vol1/finset_1.html.[8]Adam ttice of substitutions.Journal of Formalized Mathematics,9,1997./JFM/Vol9/substlat.html.[9]Andrzej Trybulec.Binary operations applied to 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