Question

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)

Answer 1

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

B - C = {a, c}

A∩(B - C) = {a, c}

A∩B = {a, c, e}

A∩C = {b, e} 

(A∩B) - (A∩C) = {a, c}

A∩(B - C) = (A∩B) - (A∩C) 

Hence proved

(ii) B∩C = {e, g} 

A - (B∩C) = {a, b, c, d}

(A - B) = {b, d}

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

(A - B)∪(A - C) = {a, b, c, d}

A - (B∩C) = (A - B)∪(A - C) 

Hence proved