If A = {1, 2, 3} and B = {2, 4}, what are A x B, B x A, A x A, B x B, and (A x B) ∩ (B x A)?
given: A = {1, 2, 3} and B = {2, 4}
To find: A × B, B × A, A × A, (A × B) ∩ (B × A)
Now,
A × B = {(1, 2), (1, 4), (2, 2), (2, 4), (3, 2), (3, 4)}
B × A = {(2, 1), (2, 2), (2, 3), (4, 1), (4, 2), (4, 3)}
A × A = {(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3)}
B × B = {(2, 2), (2, 4), (4, 2), (4, 4)}
Intersection of two sets represents common elements of both the sets
So,
(A × B) ∩ (B × A) = {(2, 2)}