# Probability of set

$$\text{Consider (A,B,C) as triplets where} A\subseteq { S }_{ 1 },~ B\subseteq { S }_{ 2 },~ C\subseteq { S }_{ 3 } [S_{1}=S_{2}=S_{3}=(1,2,3,4,.....n)]$$ such that $$A\cap B\cap C=\phi$$. Then the probability that $$A\cap B\neq \phi ,~B\cap C\neq \phi$$ when $$A\cap B\cap C=\phi$$ is $$f(n)$$.

Find $$f(2)$$

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