Question

Let A = {1,2} and B = {1,2,3,4}, C = {5,6} and D = {5,6,7,8}. Verify whether A x C is a subset of B x D?

Answer 1

Given A = {1, 2}

B = {1, 2, 3, 4}

C = {5,6}

D = {5,6,7,8}

A x C = {1,2} x {5,6}

= {(1,5) (1,6) (2, 5) (2, 6)}

B x D = {1,2, 3, 4} x {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 x C ⊂ B x D

Hence it is verified.