SOLUTION: If n(A)=13, n(A∪B)=19, and n(B)=15, what is n(A∩B)? ​ Please help.

If n(A)=13, n(A∪B)=19, and n(B)=15, what is n(A∩B)? ​




Given n(A)=13.  So n(A) = p+q = 13   

Given n(A∪B)=19.  So n(A∪B) = p+q+r = 19 

Given n(B)=15. So n(B) = q+r = 15

what is n(A∩B).  So that asks: What is q?

We have the system of equations:

 

Subtract the 1st equation from the 2nd and get r=6
Subtract the 3rd equation from the 2nd and get p=4
Substitute p=4 in the first equation and get q=9

So the Venn diagram is like this

    

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You can also do it by memorizing a formula.

n(A)=13, n(A∪B)=19, and n(B)=15, what is n(A∩B)

n(A∪B) = n(A) + n(B) - n(A∩B)
   19  =  13  +  15  -   q

   19  =  28 - q

    q  =  9

Edwin