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Question
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 values of m and n respectively are ______.
Options
7, 6
5, 1
6, 3
8, 7
Solution
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 values of m and n respectively are 6, 3.
Explanation:
Since, let A and B be such sets
i.e., n(A) = m, n(B) = n
So n(P(A)) = 2m, n(P(B)) = 2n
Thus n(P(A)) – n(P(B)) = 56
i.e., 2m – 2n = 56
⇒ 2n (2m – n – 1) = 23 7
⇒ n = 3 , 2m – n – 1 = 7
⇒ m = 6
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