If A = {a, b, c, d, e}, B = {a, c, e, g}, and C = {b, e, f, g} verify that:

(i) A ∩ (B – C) = (A ∩ B) – (A ∩ C)


(ii) A – (B ∩ C) = (A – B) ∪ (A – C)


(i) B - C represents all elements in B that are not in C


B - C = {a, c}


A(B - C) = {a, c}


AB = {a, c, e}


AC = {b, e}


(AB) - (AC) = {a, c}


A(B - C) = (AB) - (AC)


Hence proved


(ii) BC = {e, g}


A - (BC) = {a, b, c, d}


(A - B) = {b, d}


(A - C) = {a, c, d}


(A - B) (A - C) = {a, b, c, d}


A - (BC) = (A - B) (A - C)


Hence proved


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