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Q: let S={1,2,3,4} The total number of unordered pairs of disjoint subsets of S is equal to (A)26 (B)34 (C)42 (D)41pls explain what the phrase"unordered pairs of disjoint subsets mean"?
We first count the number of ordered pairs of disjoint subsets of S. For each element of S, we can choose to put it in either set A, set B, or neither (but not both), so we are making a sequence of 4 elements with 3 options each time. There are thus 3^4 different sequences ofchoices, and each results in a distinct ordered pair of subsets.As it is unordered pair- so we dont have to worry about the order. Hence,If A and B are distinct, there are exactly two ordered pairs, (A,B) and (B,A), foreach unordered pair, otherwise there is just one. Given that A and B are disjointthe only case where they are identical is when they are both empty. Thus thereare (3^4-1)/2 + 1 unordered pairs of disjoint subsets of S.The answer = 41ThanksBharat BajajIIT Delhiaskiitians faculty
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