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प्रश्न
Given A = {1, 2, 3}, B = {2, 3, 5}, C = {3, 4} and D = {1, 3, 5}, check if (A ∩ C) × (B ∩ D) = (A × B) ∩ (C × D) is true?
उत्तर
A = {1, 2, 3}, B = {2, 3, 5}, C = {3, 4} D = {1, 3, 5}
A ∩ C = {1, 2, 3} ∩ {3, 4}
= {3}
B ∩ D = {2, 3, 5} ∩ {1, 3, 5}
= {3, 5}
(A ∩ C) × (B ∩ D) = {3} × {3, 5}
= {(3, 3) (3, 5)} ….(1)
A × B = {1, 2, 3} × {2, 3, 5}
= {(1, 2) (1, 3) (1, 5) (2, 2) (2, 3) (2, 5) (3, 2) (3, 3) (3, 5)}
C × D = {3, 4} × {1, 3, 5}
= {(3, 1) (3, 3) (3, 5) (4, 1) (4, 3) (4, 5)}
(A × B) ∩ (C × D) = {(3, 3) (3, 5)} ….(2)
From (1) and (2) we get
(A ∩ C) × (B ∩ D) = (A × B) ∩ (C × D)
This is true.
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