Given n(U) = 70, n(A) = 30, n(A intersect B) = 20, n(A^1 intersect B^1) = 15 Find n(B)

Question

I really need help solving this. I have no idea how to do it

Answer 1

The statements you are given indicate the following:

• n(U)= 70, the universal set has 70 elements
• n(A)=30,  the set of A has 30 elements
• n(A∩B)= 20, this set has 20 elements, indicating that
1. the set of B has at least 20 elements
2. the set of A has 10 elements that are not in the set of B

• n(A^′ ∩ B′)= 15, this set has 15 elements, indicating that 

                   n(A U B)= n(U) - 15 = 70 - 15 =55

• Since, there are 10 elements in A that are not in B, this indicates

.             n(B)=55-10=45