Question

two finite sets have m and n elements .the total number of subsets of the first set is 48 more than the total number of subsets of the second set . the values of m and n are

Answer 1

Question :-

Two finite sets have m and n elements. The total number of subsets of the first set is 48 more than the total number of subsets of the second set . The values of m and n are?

Given :-

The total number of subsets of the first set is 48 more than the total number of subsets of the second set .

To find :-

The values of m and n are.

Required Answer :-

Value of m = 6

Value of n = 4

Solution :-

$\dashrightarrow\qquad\sf Power \: of \: Set\: 1 = 2^m(where\: m\: is \:no.\: of\: elements)$

$\dashrightarrow\qquad\sf Power \: of \: Set\: 2 = 2^n (where\: n\: is \:no.\: of\: elements)$

$\dashrightarrow\qquad\bf According\: to \: ques,$

$\dashrightarrow\qquad\sf 2^m = 48 + 2^n$

$\dashrightarrow\qquad\sf 2^m - 2^n = 48$

$\dashrightarrow\qquad\sf 2^m - 2^n = 64 - 16$

$\dashrightarrow\qquad\sf 2^6 - 2^4$

$\dashrightarrow\qquad\sf m = 6, n = 4$

Therefore,

value of m is 6 and value of n is 4.

More to know :-

Power of Set - Power of set is the collection of all subsets of a set.