离散数学第3-6章习题(中加)

《离散数学第3-6章习题(中加)》由会员上传分享，免费在线阅读，更多相关内容在教育资源-天天文库。

1、《离散数学》习题第3章1．Letbethesetofallintegers，and：，，then（　）．(A)．isainjectionandnotasurjection；　(B)．isasurjectionandnotainjection；(C)．isneitherainjectionnorasurjection；　　　(D)．isabijection．2．Letbethesetofallrealnumbers，and：，，then（）．(A)．isainjectionandnotasurjection；　(B)．is

2、asurjectionandnotainjection；(C)．isneitherainjectionnorasurjection；　　　(D)．isabijection．3．Letarerelationsonset．Whichofthefollowingpropositionsisture?（　　）．(A)．；(B)．；(C)．；　(D)．．4．Ifbeabijectionfromto，thenisabijectionfrom，and=，=．5．Let，thenthenumberofbijectionsfromtois

3、．6．Let,．WhichofthefollowingrelationsfromXtoYareorarenotfunctions?Findforfunctions．={},={},={},={},={}={}7．Let，，，find．第7页共7页8．Letbethesetofallpositiverealnumbersandbethesetofallrealnumbers，：．Showthatisabijection．9．Letbethesetofallrealnumbers，：，，．Showthatisabijecti

4、onandfind．第4章1．Letisagroupwithidentity1，where，then=,=．2．Supposeisagroup，thenforall∈,=．3．Inalgebraicsystem（isthesetofallintegersand“+”isthegeneraladdition），theidentityforwithrespecttotheoperation“+”is，thezeroelementforwithrespecttotheoperation“+”is，forany∈，＝．4．Let

5、andbethepowersetof．Inalgebraicsystem，theidentityforwithrespecttotheoperation“”is，thezeroelementforwithrespecttotheoperation“”is，theidentityforwithrespecttotheoperation“”is，thezeroelementforwithrespecttotheoperation“”is．5．Whichofthefollowingalgebraicsystemsisnotag

6、roup（　　　　）．(A)．＝{1,10}，isdefinedbymn=mn(mod11)；(B)．={1,3,4,5,9},isthesameasA；(C)．，isthegeneralmultiplication；　　　(D)．，isthegeneraladdition．6．Letbeabinaryalgebraicoperation(二元代数运算)onset．，iscalledazeroelementforunder“”if（）．(A)．forall，suchthat．(B)．forall，suchthat．(C)

7、．thereisanelement，suchthat．(D)．thereisanelement，suchthat．7．Letbeabinaryalgebraicoperation(二元代数运算)onset．，iscalledanidentity(element)forunder“”if（）．(A)．forall，suchthat．(B)．forall，suchthat．(C)．thereisanelement，suchthat．(D)．thereisanelement，suchthat．8．LetQbethesetofa

8、llrationalnumbers．Wedefineoperation“”by第7页共7页．(1)．Find；（2）FindtheidentityforQwithrespecttotheoperation；(3)．DoesinQhaveaninverse?Ifyes,pleasefind．9．Fillthefollo