Question

If n(A)=10, and n(B)=24, and n(A u B)=25, what do you know about n(A n B)?

Answer 1

Let's make a diagram to represent the situation

According to the problem, the union of A and B has 25 elements, which means there are 25 elements in total.

Then, we have 10 elements in A and 24 elements in B. Let's use the following formula

$n(A\cup B)=n(A)+n(B)-n(A\cap B)$

Let's replace the given values and solve for the intersection.

$\begin{gathered} 25=10+24-n(A\cap B) \\ n(A\cap B)=10+24-25=9 \end{gathered}$

Hence, the number of elements in the intersection is 9.