Two finite sets have m and n elements respectively. The total number of subsets of first set is 56 more than the total number of subsets of the second set. The values of m and n respectively are :

Question

Two finite sets have m and n elements respectively. The total number of subsets of first set is 56 more than the total number of subsets of the second set. The values of m and n respectively are : (A) 7, 6 (B) 6, 3 (C) 5, 1 (D) 7, 8

Tardigrade Admin · Accepted Answer

According to question, 2m-2n=56 2n(2m-n-1)=56 This is possible only, if m=6 and n=3 .

Q. Two finite sets have $m$ and $n$ elements respectively. The total number of subsets of first set is $56$ more than the total number of subsets of the second set. The values of m and n respectively are :

7, 6

6, 3

5, 1

7, 8

3, 6

According to question, $2^{m} - 2^{n} = 56$
$2^{n} (2^{m - n} - 1) = 56$
This is possible only, if $m = 6$ and $n = 3$ .

Q. Two finite sets have m and n elements respectively. The total number of subsets of first set is 56 more than the total number of subsets of the second set. The values of m and n respectively are :