Q. 8

# 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.

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