MediumMathematics
+4 / -1
Two finite sets have m and n elements respectively. The total number of subsets of first set is 120 more than the total number of subsets of the second set. The values of m and n respectively are:
A
4, 3
B
7, 3
C
6, 3
D
3, 7
Explanation
Let A and B be two sets, s.t, n(A) = m, n(B) = n. Thus, n(P(A)) = 2^m and n(P(B)) = 2^n. As per the question, n(P(A)) – n(P(B)) = 120 ⇒ 2^m – 2^n = 120 ⇒ 2^n(2^(m–n) – 1) = 128 – 8 = 2^7 – 2^3 = 2^3(2^4 – 1) ⇒ n = 3 and m – n = 4 ⇒ m = n + 4 = 7. Hence, m = 7, n = 3.
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