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

Solution:

A = {1, 2} and B = {3, 4}

Therefore, A x B = {(1, 3), (1, 4), (2, 3), (2, 4)}

Hence, n (A x B) = 4

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

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)}}

NCERT Solutions Class 11 Maths Chapter 2 Exercise 2.1 Question 8

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

Summary:

A = {1, 2} and B = {3, 4} is given. We have found that A × B = {(1, 3), (1, 4), (2, 3), (2, 4)}.The set A x B has 2⁴ = 16 subsets