Question

If A = {1, 2, 3}, B = {1, 2} and C = {2, 3}, which one of the following is correct ?

• A. (A $\times $ B) $\cap$ (B $\times $ A) = (A $\times $ C) $\cap$ (B $\times $ C)
• B. (A $\times $ B) $\cap$ (B $\times $ A) = (C $\times $ A) $\cap$ (C $\times $ B)
• C. (A $\times $ B) $\cup$ (B $\times $ A) = (A $\times $ B) $\cup$ (B $\times $ C)
• D. (A $\times $ B) $\cup$ (B $\times $ A) = (A $\times $ B) $\cup$ (A $\times $ C)

Answer 1

Answer: (C)

Given that A = {1, 2, 3}, B = {1, 2} and C = {2, 3}
A $\times$ B = {(1, 1), (1, 2), (2,1), (2, 2), (3, 1), (3, 2)}
and B $\times$ A ={(1,1), (1, 2), (1,3), (2, 1), (2, 2),(2, 3)}
$\Rightarrow $ (A $\times$ B) $\cup$ (B $\times$ A) = {(1, 1), (1, 2), (2, 1),
(2, 2), (3, 1), (3, 2), (1, 3), (2, 3)}, B $\times$ C = {(1, 2), (1, 3), (2, 2),(2,3)}
$\Rightarrow $ (A $\times$ B) $\cup$ (B $\times$ C) = {(1, 1), (1, 2), (2, 1), (2, 2), (3, 1), (3, 2), (1, 3), (2, 3)}
Hence, (A $\times$ B) $\cup$ (B $\times$ A) = (A $\times$ B) $\cup$ (B $\times$ C)