Question

Let A = {1, 2} and B = {3, 4}. Write A × B. How many subsets will A × B have? List them.

Answer 1

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)] = 2^m.

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)}