Question

Two finite sets have m and n elements respectively. The total number of subsets of first set is 96 more than the total number of subsets of the second set. The values of m and n respectively are :​

Answer 1

SET - SUBSETS

Given:

There are 2 finite sets , let say A and B .

Number of subsets of A is 96 more than the number of subsets  B have.

The number of elements in set A is m.

The number of elements in set B is n.

To Find:

The value of m and n.

Explanation:

Subset :- Set P is the subset of set Q when all the elements of P are also elements of set Q.

The formula of finding the no. of subsets of a set containing x element is $2^{x}$ .

As the number of elements in A and B are m, n respectively.

∴ number of subsets of A = $2^{m}$

and number of subsets of B = $2^n$

According to question,

$2^{m} -2^{n} =96$

$2^{m}- 2^{n}= 128-32$

$2^{m}- 2^{n}= 2^{7}- 2^{5}$

Hence, on comparing these equation, we get the value of m and n as 7 and 5 respectively.