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)}


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