Using a method of your choice, verify each of the equivalences inFigure. (a AB) = (BA a)

Using a method of your choice, verify each of the equivalences inFigure.

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(a AB) = (BA a) commutativity of A (a v B) = (B V a) commutativity of v ((a ^ 3) A7) = (a^ (BA)) associativity of A ((a V B) v 7) = (a V (3 V )) associativity of V -(¬a) = a double-negation elimination (a = 3) = (¬8 = -a) contraposition (a = B) = (-a V B) implication elimination (a + 3) = ((a = B) A (3 = a)) biconditional elimination -(a A B) = (¬a V -8) De Morgan (a V B) = (-a A-B) De Morgan (a ^ (3 Vy)) = ((a A B) V (a A)) distributivity of A over V (a V (BA Y)) = ((a V B) A (a V)) distributivity of V over A