Let S = {1, 2, 3, 4}. The total number of unordered pairs of disjoint subsets of S is equal to (A) 25 (B) 34 (C) 42 (D) 41

ans :- (D) 41

because Each element in either (A) or (B) or neither

So total ways = 3⁴ = 81

A = B if A = B = Φ (1 case)

otherwise A and B are interchangeable.

 so n = 1 +(81-1)/2 = 41