Part e) and f) please 12 marksl/ (e)Let A and B be sets. Prove that A \\ (A \\ B

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Part e) and f) please

12 marksl/ (e)Let A and B be sets. Prove that A (A B) = A 3. 3 marks] , construct an appropriate map and show that it is a (f) Using the above definition of ebijection to prove that if n,r NU(O with n 2 T, then n-r [4 marks] B12. (a) Let A and B be sets. Define the Cartesian product A x B. ii) Let A = {(m-n) : n E Z} and B = {(n, n +2) : n E Z} (both subsets of Z × Z). White down A B. 13 marks] [6 marks] n+r and 0 r S n-1. You DO (b)By reducing modulo 7, show that 21x5+3y2 = 11 has no integer solutions x and y. ' marks) 0 c) Let a, n N. Show that there exist q,r Z such that a NOT have to show that a and r are unigue

Explanation / Answer

Answer of (e)

By definition A B=A Bc

Hence A (A B) = A (A B)c = A (A Bc) c = A (Ac B) = (A Ac)(A B) = (A B) = A B

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