If S = {1, 2, 3, 4}, then the total number of unordered pairs of disjoint subsets of S is (1) 25 (2) 34 (3) 42 (4) 41

Solution: (4)

S = {1, 2, 3, 4}

According to the definition of disjoint sets, if there exist two sets A and B, A ⋂ B = ɸ.

Every element of S can be an element of A or of B or of neither of the subsets. 

There exist 3 possibilities for each element.

Since there are for 4 elements, there are 34 possibilities are present. 

Total number of ordered pairs of subsets = 34 + 1 

= 81 + 1

= 82

Total number of unordered pairs = 82 / 2 = 41

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