Question

how to do these five problems

4- Zeis a multiple } 1) Let Boteze is a multiple of 4 a) Prove that ASB b) Is BCA? Prove or disprove. 2) Let 4-CZ-3 scade Prove that A is equal to the set of even numbers. - PC-+7,rcz} 3) Let - EZ-4+3, rez} a) List 5 elements of A and 5 elements of B b) Is AC ? Prove or disprove. c) Is BC? Prove or disprove 4) Prove that Is #ICA A - PEZA - 4+1, rez} 5) Let -fez-4+9.rez} Prove that 4-3 4- PEZIN 3+1,182) 6) Let - CZA= 3+2,7E2} Show that A and B have no elements in common. 1891 I To Do Calendar Notifications Inbox

how to do these 6 problems

Answer 1

corrido A= (ne zln is multiple of af 1 = {nez/n=4t, ZEZE APL -16,72; -8, -4,0,4, 8, 12, 16, B= jnez/in is multiple of all so ={nez/n = 4t, tez's - Inez (n=+2JE, ZEZZ} : B= (----8,-4, 56, 0, 4,6,87734 t=4=;n=4, 2=9=) = 6 ( n²=16 . . 5236 t=16=10=8-- : 264 @ clearly Bori o t© ASB MEA n=4t fantez . - ก=6 = n244te) where kezt en is multiple of a =) NEB

AMEA = MEB Ynez ACB O since let me B be any pait Thon n²is multiple of 4 n=4t for rezt >n=+25t fa tezt = nis multiple of & anda. Hence B&A - By Beeing Bets A & B Bom 04 clearly B does not contained in A ® 4-1 nez/nts is odd} = 1 nez/n+8=2H, KERY = nez In=2K+-3, KEZE = { nez/n= 262, KERG

=/nez/n=2(K), KEZE =Inezin is an even intogors A=&et of even numbers ③ A= Phez/n=847, HELG A=/---, -17,3,4,7,15,23; B=1 hez/n=42+3, teze ----9; -6,-1,3,7,11,157--of

O tlearly by selling * t© - ASB 1. let net =) n=847 n=41217+4+3 an=4127)+3. =) = 4hts where haltez =) NEB © ASB beit let neB 1. Then nachts n can not be written as 847 =) n& 847 =) n&a B&A "clearly by seeing & 4@, B&A

@ Дc B(- АПВ-А (ANB)'SA! < AluBl=A! =) Blea ACB ca) BICA! o A={nez/n=4241, teze Az ----|, 7-5,1,5933, 17. B = {ne 24 n=4244, teze B=1---11,7-5,1,5,9,13,17 -- of Bom 6 46, -A B ® A={nez/n=3th, here A={----; 8; 5,2,1,4,7,10. By nez/ n=37+2, teZGU BOY----7,-4,-1,2,5,8,1,..ng Hence AnB= . TH AAB have no common elemente