Question

Two finite sets have m and n elements respectively. The total number of subsets of first is 24 more than the total number of subsets of second set. Find the values of m and n.

Answer 1

Answer:

m=5, n=3

Step-by-step explanation:

Subsets of a set with x elements is: 2^x

Here, Let Set A has m elements and Set B has n elements.

ATQ:

2^m= 24+ 2^n

2^m-2^n = 24

Now, if 2^m=24+2^n, it implies 2^m>2^n        therefore, m>n

And m and n must be integral as well, as no of elements cannot be fractional.

There is only 1 possibility: m=5 and n=3.