(i) Given:

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

BC = {e, o} and A(BC) = {a, e, I, o, u}

B

C

RHS:

AB = {a, d, e, I, o, u, v} and AC = {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}.

BC = {a, d, v, e, o, t, m} and A(BC) = {a, e, o}

B

C

RHS:

AB = {a, e, o} and AC = {e, o}

(A ∩ B) ∪ (A ∩ C) = {a, e, o}

LHS = RHS. [Verified]