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प्रश्न
If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {4, 5, 6, 7, 8} and universal set X = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, then verify the following:
(A ∪ B)' = (A' ∩ B)'
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उत्तर
A ∪ B = {1, 2, 3, 4} ∪ {3, 4, 5, 6}
= {1, 2, 3, 4, 5, 6}
∴ (A ∪ B)' = {7, 8, 9, 10} ...(1)
Now, A' = {5, 6, 7, 8, 9, 10} and
B' = {1, 2, 7, 8, 9, 10}
∴ A' ∩ B' = {5, 6, 7, 8, 9, 10} ∩ {1, 2, 7, 8, 9, 10}
= {7, 8, 9, 10} ...(2)
From (1) and (2), we get,
(A ∪ B)' = (A' ∩ B)'
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