Let $S=\{1,2,3,4\}$. The total number of unordered pairs of disjoint subsets of $S$ is equal to

Let $S=\{1,2,3,4\}$. The total number of unordered pairs of disjoint subsets of $S$ is equal to
  1. 25
  2. 34
  3. 42
  4. 41

Solution

Let $A \cap B=\phi, A, B \subset S$ $ \begin{aligned} & 3^4=\frac{81+1}{2}=41 \\ \Rightarrow \quad & \frac{3^4+1}{2}=41 \end{aligned} $

Asked in: JEE Advanced 2010 (Paper 2)

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