Question

Two finite sets have m and n elements. The total number of subsets of the first set is 112 more than the total number of subsets of the second set. Find the valuesof m and n.

Answer 1

m=6 and n=3…

As,

no. of subsets which has element m = 2^m

No. Of subsets which has element n = 2^n

So, ATQ

2^m= 2^n +56

2^m - 2^n = 2³.7

(2^n /2^n . 2^m) - 2^n = 2³.7

2^n ( 2^m-n - 1) = 2³.7

Now, on comparing

We get,

2^n = 2³ or

n=3 ……(i)

S.o,

2^m-n -1= 7

2^m-n=8

2^m-n= 2³ or

m-n= 3

m-3= 3. From(i)

m=6