Q.

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

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a

25

b

34

c

42

d

41

answer is D.

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Detailed Solution

The total number of ordered pairs of disjoint subsets of S , except ordered pair (ϕ,ϕ) is (C40×24+C41×23+C42×22×C43×21+C44×20)–1 = (1+2)4–1=80 ∴   Total number of unordered pairs of disjoint subsets of S is equal to 802+1 =41 .
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Let S ={1,2,3,4}. The total number of unordered pairs of disjoint subsets S is equal to