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 .