Let U be a universal set with subsets A and B such that n(U)=121, n(A)=65, n(B′)=73, and n(A∩B)=18. Find the following:(1) n(B)= (2) n(A∪B)= (3) n((A∩B)′)=

Answer 1

With n sets, if we have 2^n conditions, as long as they aren't redundant, we can figure out every possible set combination. In this case, 2^n = 2^2 = 4. We shall not figure out the cardinality of each of the 2^n disjoint subsets to solve this problem, however, to solve this problem.

1) n(B) = n(U) - (B') = 121 - 73 = 48

2) n(A U B) = n(A) + n(B) - n(AB) = 65 + 48 - 18 = 95

3) n((AB)') = n(U) - n(AB) = 121 - 18 = 103