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