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प्रश्न
Let A = {1, 2} and B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}. Verify whether A × C is a subset of B × D?
उत्तर
Given A = {1, 2}
B = {1, 2, 3, 4}
C = {5, 6}
D = {5, 6, 7, 8}
A × C = {1, 2} × {5, 6}
= {(1, 5) (1, 6) (2, 5) (2, 6)}
B × D = {1, 2, 3, 4} × {5, 6, 7, 8}
= {(1, 5) (1, 6) (1, 7) (1, 8) (2, 5) (2, 6) (2, 7) (2, 8) (3, 5) (3, 6) (3, 7) (3, 8) (4, 5) (4, 6) (4, 7) (4, 8)}
∴ A × C ⊂ B × D
Hence it is verified.
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