Question

LetA = {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

Weknow that if C is a set with n(C)= m,then n[P(C)]= 2^m.

Therefore,the set A × 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)}