Let A = {10, 15, 20, 25, 30, 35, 40, 45, 50}, B = {1, 5, 10, 15, 20, 30} and C = {7, 8, 15, 20, 35, 45, 48}. Verify A (B ⋂ C) = (A B) ⋃ (A C).

To do this consider,

B ⋂ C = {1, 5, 10, 15, 20, 30} ⋂ {7, 8, 15, 20, 35, 45, 48}

= {15, 20}

⇒ A (B ⋂ C) = A {15, 20}

= {10, 25, 30, 35, 40, 45, 50} … (1)

Now, A B = {10, 15, 20, 25, 30, 35, 40, 45, 50} {1, 5, 10, 15, 20, 30}

= {25, 35, 40, 45, 50}

And A C = {10, 15, 20, 25, 30, 35, 40, 45, 50} {7, 8, 15, 20, 35, 45, 48}

= {10, 25, 30, 40, 50}

Then, (A B) ⋃ (A C) = {25, 35, 40, 45, 50} ⋂ {10, 25, 30, 40, 50}

= {10, 25, 30, 35, 40, 45, 50} … (2)

From (1) and (2), it follows that A (B ⋂ C) = (A B) ⋃ (A C).

Hence, verified.