SOLUTION: I am having problems understanding how to show the answer to this problem. If If n(A)= 15, n(A n B)=5, and n(A u B)=30, then what is n(B)? I know the answer is 20, I just am not

Algebra ->  Subset -> SOLUTION: I am having problems understanding how to show the answer to this problem. If If n(A)= 15, n(A n B)=5, and n(A u B)=30, then what is n(B)? I know the answer is 20, I just am not       Log On


   

Question 705548: I am having problems understanding how to show the answer to this problem. If
If n(A)= 15, n(A n B)=5, and n(A u B)=30, then what is n(B)? I know the answer is 20, I just am not sure of how I got the result. Can you help me?
Answer by jerryguo41(197) About Me  (Show Source):
You can put this solution on YOUR website!
n(A) is the population of "A"'s
That includes:
- n(A n 'B) (A and not B)
- n(A n B) (Both A and B)
So, if n(A n B)=5 and n(A)=15:
n(A n 'B)= 10
Thus is n(A u B)=30 and n(A n 'B)=10:
n(B)= 20
-------------------------------------
Think of this as a venn diagram
The left two sections would be called n(A)= 15
The middle section would be n(A n B)=5
Thus the left section would be n(A n 'B) = 10
Finally of both the far left and the far right sections n(A u B)=30;
n(A u B) - n(A n 'B) = n(B)
30 - 10 = 20