2. A,B,C are subsets of a universal set S. Prove that
(i) [AN(BUC) n(A'U(B'n c')] = 0,
(ii) (ANB) U(ANB) U (A'N B)U(A'N B') = S,
(ii) (AUB) n(AU B') n (AUB) = An B,
(iv) (AN BOC) U (AN BN C') U(An B' nC)u(An B'n c') = A,
(v) (AUBUC) n(AUBUC') N (AU B'UC) n(AU BUC) = (AUB) n
(BUC) (CU A).
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