Question

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

• A. (A $×$ B) $âˆ\copyright$ (B $×$ A) = (A $×$ C) $âˆ\copyright$ (B $×$ C)
• B. (A $×$ B) $âˆ\copyright$ (B $×$ A) = (C $×$ A) $âˆ\copyright$ (C $×$ B)
• C. (A $×$ B) $∪$ (B $×$ A) = (A $×$ B) $∪$ (B $×$ C)
• D. (A $×$ B) $∪$ (B $×$ A) = (A $×$ B) $∪$ (A $×$ C)

Answer 1

Answer: (C)

Given that A = {1, 2, 3}, B = {1, 2} and C = {2, 3}
A $×$ B = {(1, 1), (1, 2), (2,1), (2, 2), (3, 1), (3, 2)}
and B $×$ A ={(1,1), (1, 2), (1,3), (2, 1), (2, 2),(2, 3)}
$⇒$ (A $×$ B) $∪$ (B $×$ A) = {(1, 1), (1, 2), (2, 1),
(2, 2), (3, 1), (3, 2), (1, 3), (2, 3)}, B $×$ C = {(1, 2), (1, 3), (2, 2),(2,3)}
$⇒$ (A $×$ B) $∪$ (B $×$ C) = {(1, 1), (1, 2), (2, 1), (2, 2), (3, 1), (3, 2), (1, 3), (2, 3)}
Hence, (A $×$ B) $∪$ (B $×$ A) = (A $×$ B) $∪$ (B $×$ C)