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

1.	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» (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.

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»

(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.