Trouble with sets

[MSkaggs87]

Hey all,
Here's my problem:

Let A and B be subsets of a universal set U: n(U)=60, n(B)=25, and n(AUB')=45. Find n(AintersectB) and n(A'intersectB). Any ideas?

 

[soroban]

Hello, MSkaggs87!

If you sketch a Venn diagram, it may help you follow my reasoning.

Let A and B be subsets of a universal set U: n(U)=60, n(B)=25, and n(A U B')=45.

Find: n(A ∩ B) and n(A' ∩ B).

From DeMorgan's Laws, the complement of A U B' is A' ∩ B

Since n(U) = 60 and n(A U B') = 45, then n(A' ∩ B) .= . 60 - 45 .= .15

Since n(B) = 25 and n(A' ∩ B) = 15, then n(A ∩ B) = 10