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Let S={1,,2,3,4} . The total number of u...

Let `S={1,,2,3,4}` . The total number of unordered pairs of disjoint subsets of `S` is equal

A

25

B

34

C

42

D

41

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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