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Question
If A = {1, 2, 3, 4, 5}
B = {2, 4, 6, 8}
and C = {3, 4, 5, 6}
Verify : A - (B ∪ C) = (A - B) ∩ (A - C)
Solution
A = {1, 2, 3, 4, 5}
B = {2, 4, 6, 8}
C = {3, 4, 5, 6}
B ∪ C = {2, 4, 6, 8} ∪ {3, 4, 5, 6}
= {2, 3, 4, 5, 6, 8}
A - (B ∪ C) = {1, 2, 3, 4, 5} - {2, 3, 4, 5, 6, 8}
= {1}
A - B = {1, 2, 3, 4, 5} - {2, 4, 6, 8}
= {1, 3, 5}
A - C = {1, 2, 3, 4, 5} - {3, 4, 6, 8}
= {1,2}
∴ (A - B) ∩ (A - C) = {1, 3, 5} - {1,2}
= {1}
∴ A - (B ∪ C) = (A - B) ∩ (A - C)
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