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A,C,G please 1. Let A, B, and C be subsets of some universal set u. Prove the following statements from Theorem 4.2.6 (a) AUA=/1 and AnA=A. (b) AUO- A and An. (c) AnB C A and ACAUB (d) AU(BUC)= (A U B) U C and An(B n C)-(A n B) n C. (e) AUB=BUA and A n B = B n A. (f) AU(BnC) (AU B) n(AUC) (g) (A U B) = A n B (h) AUA=1( and An-=0. hore...

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Let U be a set, and let A CU. Recall the indicator function XA: U + Z, defined by XA(x) = ſi, rEA 0, A. Now, let A, B CU and consider the symmetric difference of A and B defined by A AB= (A - B)U(B - A). (a) Show that AAB CU, and compute Ø A A. (b) Prove that Ve EU, XAAB(C) = XA(2) + XB(2), where addition is taken modulo 2 (so that 1+1 = 0).

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