Question

Let A = (1, 2}, B = [1, 2, 3, 4}, C = { 5, 6} and D = (5, 6, 7, 8}. Verify that 

(i) A x (B∩C) = (A x B)∩(A x C). 

(ii) A x C is a subset

Answer 1

(i) B ∩ C = { } 

∴ A x (B ∩ C) = φ ………….. (1)

A x B = {(1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (2, 3), (2,4)} 

A x C = {(1, 5), (1,6), (2, 5) (2,6)} 

∴ (A x B) ∩ (A x C) = φ ………………. (2) 

From (1) and (2), we get 

A x (B∩C) = (A x B) ∩(A x C) 

(ii) A x C = {(1, 5), (1,6), (2, 5), (2, 6)} 

B x D = {(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)}. 

Clearly every elements of A x C is an element of B x D. A x C ⊂B x D.