Two finite sets have 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 values of m and n are:

Question

Two finite sets have 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 values of m and n are: (A) 7, 6 (B) 6, 3 (C) 5, 1 (D) 8, 7

Tardigrade Admin · Accepted Answer

Given: Two finite sets have m and n elements ∴ 2 m -2 n =56 ⇒ 2 m -2 n =64-8 ⇒ 2m-2n=26-23 ⇒ m=6, n=3

Q. Two finite sets have $m$ 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 values of $m$ and $n$ are:

7, 6

6, 3

5, 1

8, 7

Given: Two finite sets have $m$ and $n$ elements
$∴ 2^{m} - 2^{n} = 56$
$\Rightarrow 2^{m} - 2^{n} = 64 - 8$
$\Rightarrow 2^{m} - 2^{n} = 2^{6} - 2^{3}$
$\Rightarrow m = 6, n = 3$

Q. Two finite sets have 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 values of m and n are: