Two finite sets have m and n elements respectively.


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 value of m and n is respectively are:

(a) 7, 6

(b) 5, 1

(c) 6, 3

(d) 8, 7


Let us suppose two finite sets are A and B
Let A has elements

Let B has n elements

Then total number of subjects of A is 2m and total number of subjects of B is 2n.

According to given condition,

2m – 2n = 56

i.e 2n (2m – n – 1) = 56

Since 56 = 8 × 7

$=2^{3} \times 7$

i.e. $2^{n}\left(2^{m-n}-1\right)=2^{3} \times 7$

i.e $n=3$ and $2^{m-n}-1=7$

i.e $2^{m-n}=8$


i.e. m – n = 3

i.e m = n + 3

m = 6

i.e m = 6, = 3

Hence, the correct answer is option C.

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