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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.
(A) 7, 6
(B) 5, 1
(C) 6, 3
(D) 8, 7
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.
(A) 7, 6
(B) 5, 1
(C) 6, 3
(D) 8, 7
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.
(A) 7, 6 (B) 5, 1 (C) 6, 3 (D) 8, 7
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.
(A) 7, 6 (B) 5, 1 (C) 6, 3 (D) 8, 7
The correct answer is (C).
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