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).
Answer :
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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