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Two finite sets P and Q have m and n elements respectively. The total number of subsets of P exceeds the total number of subsets of Q by 56. Find the value of (m + n).
- 13
- 9
- 10
- 15
Correct answer: 9
Solution
The number of subsets of a set with k elements is 2^k. Setting 2^m - 2ⁿ = 56 and factoring gives 2ⁿ(2^(m-n) - 1) = 8*7, so n=3 and m=6, hence m+n=9.
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