Question

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

Answer 1

A = {1, 2} and B = {3, 4}
∴A x B = {(1, 3), (1, 4), (2, 3), (2, 4)}
⇒ n(A x B) = 4
We know that if C is a set with n(C) = m, then n[P(C)] = 2m
Therefore, the set A x B has 24= 16 subsets.
These are:
Φ, {(1, 3)}, {(1, 4)}, {(2, 3)}, {(2, 4)}, {(1, 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)}