Discrete Math - Set Theory, Membership Tables and Set Identites

5. Use membership tables (i.e., no set identities or Venn diagrams) to demonstrate that ((AUC)nB) u ((C - D)n B) and are equivalent expressions (5 marks) 6. Use set identities (i.e., no membership tables or Venn diagrams) to demonstrate that ((A uC)- (Anc)) - (An B) and are equivalent expressions (5 marks) TABLE EXAMPLE 1 0 0 0 1 1 0 1 00 0 0 10 0 0 0 0 SET IDENTITES 0 dentity Law: AU0-A, AnU-A . Idempotent Law. A U A-A, A A = A . Domination Law: A U U = U, A 0-0 . Complementation Law: A- A Commutative Law: AUB- BUA, AnB- BnA . Associative Law: A U (BU C) (A U B) U C , A (Bn C) ( BC . Distributive Law: A (BU C) ( B) U ( C) , A U (Bn C) (A UB) n(A U C) . Absorption Law: A U (A B) A and A (A U B) A . De Morgan's Law: A B-A U B. A U B A B . Complement Law. A U A = U, A A = 0 . Difference Equivalence: A \ B-A B