# Counting the Number of Elements of a Set.

Define sets $$A_i =\{i, i+1\}$$ and $$B_i=\{A_1, A_2,.....,A_i\}.$$

$$F_i$$ is the set of all possible sets that can be formed by taking union of one or more elements of $$B_i$$. For example, $$F_2 =\{A_1, A_2, A_1\cup A_2\}.$$

Find the number of distinct elements of $$F_{15}$$.

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