Question

Two finite sets A and B are having m and n elements. The total number of subsets of the first set is 56 more than the total number of subsets of the second set. The value of m and n are
1. 7, 6
2. 6, 3
3. 5, 3
4. 8, 7

Answer 1

Correct Answer - Option 2 : 6, 3

Concept:

• If a set contains n elements, then the total number of subsets will be 2n

 

Calculation:

Total number of subsets of the first is 2m while total number of subsets of the second is 2n.

Now it is given that

2m = 2n + 56

⇒ 2m - 2n = 56

⇒ 23(2m-3 - 2n-3) = 56

⇒ (2m-3 - 2n-3) = 7

⇒ (2m-3 - 2n-3) = 8 - 1

⇒ (2m-3 - 2n-3) = 23 - 20

Hence compare the terms,

m - 3 = 3 thus m = 6 and

n - 3 = 0 giving n = 3.

Hence, (m, n) = (6, 3)