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Two finite sets have m and n elements. T...

Two finite sets have m and n elements. The total number of subsets of the first set is 48 more than the total number of subsets of the second set. The value of m - n is

A

25

B

41

C

6

D

9

Text Solution

Verified by Experts

The correct Answer is:
D
For disoint sets, `AnnB=phi`
Each element in either A or B or neither.
`therefore` Total ways `=3^(4)=81,A=B" iff "A=B=phi`
Otherwise, A and B are interchangable
`therefore` Number of unordered pair for disoint subsets of
`S=(3^(4)+1)/(2)=41`
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