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  • Two finite sets have m and n elements. The number of subsets of the first set is 112 more than that of the second set. The values of m and n are, respectively, (a) 4,7 (b) 7,4 (c) 4,4 (d) 7, 7

Two finite sets have m and n elements. The number of subsets of the first set is 112 more than that of the second set. The values of m and n are, respectively, (a) 4,7 (b) 7,4 (c) 4,4 (d) 7, 7
 

Answers (1)

According to the question we have,

            \\2^m -2^n = 112 \\ \quad 2^n(2^{m-n} - 1) = 2^4\times 7\\ 2^n = 2^4 \text{ and } 2^{m-n} -1 = 7\\ n = 4\text{ and } 2^{m-n} = 1+7 = 8 = 2^3 \\ n+4\text{ and } m-n = 3 \\ m = 7

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