Use the set identities in Table 1 to prove the following identities (be sure to give...

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Use the set identities in Table 1 to prove the following identities (be sure to give the identity being used at each step): (a) (AUB)UA = A (b) An (B-C)= (ANB) - (ANC) Table 1 Identity ANU=A AUB=A AUU=U A00=0 AUA = A ANA A (A) = A AUB BUA AOB BOA AU (BUC) = (AUB) UC An (BOC)=(ANB) NC AU (BOC) = (AUB) n(AUC) An (BUC) = (ANB) U (ANC) ACB AUB AUB ANB = AU (ANB) = A An (AUB) = A AUĀ=U ANĀ=0 Name Identity laws Domination laws Idempotent laws Complementation law Commutative laws Associative laws Distributive laws De Morgan's laws Absorption laws Complement laws Use the set identities in Table 1 to prove the following identities (be sure to give the identity being used at each step): (a) (AUB)UA = A (b) An (B-C)= (ANB) - (ANC) Table 1 Identity ANU=A AUB=A AUU=U A00=0 AUA = A ANA A (A) = A AUB BUA AOB BOA AU (BUC) = (AUB) UC An (BOC)=(ANB) NC AU (BOC) = (AUB) n(AUC) An (BUC) = (ANB) U (ANC) ACB AUB AUB ANB = AU (ANB) = A An (AUB) = A AUĀ=U ANĀ=0 Name Identity laws Domination laws Idempotent laws Complementation law Commutative laws Associative laws Distributive laws De Morgan's laws Absorption laws Complement laws