Question

two finite sets have ‘m’ and ‘n’ elements. The total number of subsets of the first is 56 more than the total number of subsets of the second set. The values of m and n are​

Answer 1

Answer:

Let A has m elements

Let B has n elements

Total number of students of A=2^m

 

Total number of students of B=2^n

 

It is given ⇒2^m −2^n =56

2^n (2  m−n  −1)=56

⇒2^n  =even and 2^m−n  −1=0 odd

Now,

56=8×7=2^3  ×2^7

 

⇒2^n  (2^m−n −1)=2^3  ×7

⇒n=3

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Now, 8(2^m−3 −1)=8×7

⇒2^m−3  −1=7

⇒2^m−3

=8=2^3

⇒m−3=3

⇒m=6.

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I HOPE IT HELPS !!!!!