NCERT Solutions
Class 11 Maths
Relations and Functions

Ex.2.1 Q.8
Let A = {1, 2} and B = {3, 4}. Write A × B. How many subsets will A × B have? List them.
A = {1, 2} and B = {3, 4}
So, 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.
Therefore, the set A × B has 24 = 16 subsets. These are
ф, {(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)}