Question

2 finite sets have 'm' and 'n' elements . The number of subsets of first is 48 more than the number of subsets of second set .Then what is m and n

Answer 1

The number of subsets of the first set is 112more than that of the second set. Two finite sets have m and n elements. The number of subsets of the first set is 112 more than that of the second set. The values of m and n are, respectively, (a) 4,7 (b) 7,4 (c) 4,4 (d) 7, 7 

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Answer 2

Step-by-step explanation:

Let A has m elements

Let B has n elements

Total number of students of A=2m

Total number of students of B=2n

It is given ⇒2m−2n=56

2n(2m−n−1)=56

⇒2n=even and 2m−n−1=0 odd

Now,

56=8×7=23×27

⇒2n(2m−n−1)=23×7

⇒n=3

Now, 8(2m−3−1)=8×7

⇒2m−3−1=7

⇒2m−3=8=23

⇒m−3=3

⇒m=6.