NIMCET 2016 Question Paper with solutions

Question : 74 of 120

Marks: +1, -0

Two finite sets A and B are having m and n elements. The total numbers 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;

7, 6
6, 3
8, 7
6, 8

Validate

Solution:

Let the total number of subset in set

A=2^m

and subset in s

B=2^n

According to the given condition,

2^m=2^n+56

⇒2^m-2^n=56

⇒2^n(2^{m-n}-1)=8×7

⇒2^n(2^{m-n}-1)=2^3×(2^3-1)

On comparing both sides, we get

n=3

and

m-n=3

⇒m-3=3

⇒m=6

So,

m=6

and

n=3

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