A = {1, 2, 4, 5} B = {2, 3, 5, 6} C = {4, 5, 6, 7}.

Now,

B ∪ C = {5, 6}

A ∩ (B ∪ C) = {5}

Similarly finding out R.H.S we get,

A ∩ B = {2, 5}

A ∩ C = {4, 5}

(A ∩ B) ∩ (A ∩ C) = {5}

L.H.S = R.H.S

Hence, Verified.