Question

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?

Answer 1

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.