Sets and Relations Part 1

$\because (B \cup C)' = B' \cap C'$$B'$ is a set containing sub sets of $A$ containing element 1 and not containing 2.And $C'$ is a set containing subsets of $A$ whose sum of elements is not prime.So, we need to calculate number of subsets of $\{3,4,5,6,7\}$ whose sum of elements plus 1 is composite.Number of such 5 elements subset $=1$Number of such 4 elements subset $=3$ (except selecting 3 or 7 )Number of such 3 elements subset $=6$ (except selecting $\{3,4,5\},\{3,6,7\},\{4,5,7\}$ or $\{5,6,7\}$ )Number of such 2 elements subset $=7$ (except selecting $\{3,7\},\{4,6\},\{5,7\}$ )Number of such 1 elements subset $=3$ (except selecting $\{4\}$ or $\{6\}$ )Number of such 0 elements subset $=1$$n(B' \cap C') = 21 \Rightarrow n(B \cup C) = 2^7 - 21 = 107$