Two finite sets have m and n elements respectively. The total number o

1.	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
Answer» 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)) = 2^m , n (P(B)) = 2ⁿ Thus n (P(A)) – n (P(B)) = 56, i.e., 2^m – 2ⁿ = 56 ⇒ 2ⁿ (2^{m – n} – 1) = 2³ 7 ⇒ n = 3 , 2^{m – n} – 1 = 7 ⇒ m = 6

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

Answer»

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)) = 2^m , n (P(B)) = 2ⁿ

Thus n (P(A)) – n (P(B)) = 56, i.e., 2^m – 2ⁿ = 56

⇒ 2ⁿ (2^{m – n} – 1) = 2³ 7

⇒ n = 3 , 2^{m – n} – 1 = 7

⇒ m = 6