Question

By taking suitable sets A, B, C, verify the following results:

(B − A) ∩ C = (B ∩ C) − A = B ∩ (C − A)

Answer 1

To prove the following results let us take U = {1, 2, 5, 7, 8, 9, 10}

A = {1, 2, 5, 7}

B = {2, 7, 8, 9}

C = {1, 5, 8, 7}

To prove (B – A) ∩ C = (B ∩ C) – A = B ∩ (C – A)

A = {1, 2, 5, 7}, B = {2, 7, 8, 9}, C = {1, 5, 8, 10}

Now B – A = {8, 9}

(B – A) ∩ C = {8}   ......(1)

B ∩ C = {8}

A = {1, 2, 5, 7}

So (B ∩ C) – A = {8} ......(2)

C – A = {8, 10}

B = {2, 7, 8, 9}

B ∩ (C – A) = {8} ......(3)

(1) = (2) = (3)