Let A and W be sets. Suppose n(A′)=17, n(W)=12 , n(A′∪W′)=25 and n(A∩W)=3. What is n(U)
U=(A∩W)∪(A∩W)′(A∩W)∩(A∩W)′=∅⇒|U|=|(A∩W)|+|(A∩W)′||A∩W|=3|(A∩W)′|=|(A′∪W′)|=25|U|=3+25=28
as far as I can see the other details aren't needed.