# Counting the Number of Elements of a Set.

**Discrete Mathematics**Level 5

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 \(F_{15}\).