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Question
Let A = {1, 2} and B = {3, 4}. Write A × B. How many subsets will A × B have? List them.
Solution
A = {1, 2} and B = {3, 4}
A × B = {(1, 3), (1, 4), (2, 3), (2, 4)}
⇒ n(A × B) = 4
We know that if C is a set with n(C) = m, then n[P(C)] = 2m.
A × B number of bats = 24 = 16
Element of subset A x B = H, {(1, 3)}, {(1, 4)}, {(2, 3)}, {(2, 4)}, {(1, 3), {3),
(1, 4)}, {(1, 3), (2, 3)}, {(1, 3), (2, 4)}, {(1, 4), (2, 3)}, { (1,4), (2,4)}, {(2, 3),
(2, 4)}, {(1, 3), (1, 4), (2, 3), {(1, 3), (1, 4), (2, 4)}, {(1) , 3), (2, 3), (2, 4)}, {(1,4), (2, 3), (2, 4)}, {(1, 3), (1, 4),, (2, 3), (2,4)}
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