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Question

Two finite sets A and B have m and n elements, respectively. If the total number of subsets of A is112 more than the total number of subsets of B, then the value of mis


A

7

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B

9

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C

10

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D

12

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E

13

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Solution

The correct option is A

7


Find the value of m:

Given,

The number of subsets of Ais 112 greater than the number of subsets of B

Now,

2m-2n=1122n(2m-n-1)=24×7

Now, on comparing both sides

2n=24and 2m-n-1`=7

So, n=4.......(1)

2m-n-1=72m-n=82m-n=23m-n=3......(2)

Now, from (1) and (2)

m=7

Hence, the correct answer is (A).


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