Let A a b d e B b c e f and C d e f g Verify A B C A B A

Let A = {a, b, d, e}, B = {b, c, e, f} and C = {d, e, f, g}

Verify A (B C) = (A B) (A C)

Verify A (B C) = (A B) (A C)

Solution

i) For verifying A (B C) = (A B) (A C)

Considering LHS

A (B C) = {a, b, d, e} {b, c, d, e, f, g} = {b, d, e}

RHS

(A B) (A C) = {b, e} {d, e} = {b, d, e}

clearly, LHS = RHS, hence verified.

ii) for verifying A (B C) = (A B) (A C)

considering LHS

A (B C) = {a, b, d, e} {e, f} = {a, b, d, e, f}

RHS

(A B) (A C) = {a, b, c, d, e, f} {a, b, d, e, f, g} = {a, b, d, e, f}

Clearly, LHS = RHS, thus verified.