Sets and Relations Part 1

∵(B∪C)′=B′∩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′∩C′)=21⇒n(B∪C)=27−21=107