Question

Let A = {a, e, I, o, u}, B = {a, d, e, o, v} and C = {e, o, t, m}. Using Venn diagrams, verify the following 

(i) A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C) 

(ii) A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C).

Answer 1

(i) Given: 

A = {a, e, I, o, u}, B = {a, d, e, o, v} and C = {e, o, t, m}. 

B∩C = {e, o} and A∪(B∪C) = {a, e, I, o, u}

RHS:

A∪B = {a, d, e, I, o, u, v} and A∪C = {a, e, I, o, u, t, m}

(A∪B)∩(A∪C) = {a, e, I, o, u}

LHS = RHS. [Verified].

(ii) Given: 

A = {a, e, I, o, u}, B = {a, d, e, o, v} and C = {e, o, t, m}.

B∪C = {a, d, v, e, o, t, m} and A∩(B∪C) = {a, e, o}

RHS: 

A∩B = {a, e, o} and A∩C = {e, o}

(A ∩ B) ∪ (A ∩ C) = {a, e, o} 

LHS = RHS. [Verified]