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. 5, 1
• C. 6, 3
• D. 8, 7

Answer 1

The correct option is C 6, 3

$\mathrm{Given}\mathrm{that}n\left(A\right)=m,n\left(B\right)=nn\left(P\right(A\left)\right)=2^m\mathrm{and}n\left(P\right(B\left)\right)=2^n\mathrm{Thus},n\left(P\right(A\left)\right)-n\left(P\right(B\left)\right)=2^m-2^n=562^n\left(2^{m-n}-1\right)=2^3\cdot 7\mathrm{Comparing}\mathrm{both}\mathrm{sides},\mathrm{we}\mathrm{get};n=3\therefore 2^{m-n}-1=7\Rightarrow 2^{m-n}=8=2^3\Rightarrow m-n=3\Rightarrow m-3=3\mathrm{or},m=6$