JEE Advanced 2010 Mathematics question

Let . The total number of unordered pairs of disjoint subsets of S is equal to

(A)25
(B)34
(C)42
(D)41Correct

Answer: (D)

Solution

First count ordered pairs (A, B) of disjoint subsets. Each element of S has exactly three choices: it belongs to A only, to B only, or to neither (it cannot belong to both). So the number of ordered pairs is . In an unordered pair {A, B}, the ordered pairs (A, B) and (B,

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Question ID VK-025838