Question

Given n(A) = 288, n(B) = 183, and n(AU B) = 434, find n(A∩ B).a) 37b) None of thesec) 539d) 329

Answer 1

We have to find n(A∩B), which is the number of elements that belong both to A and B.

We can use the following relation:

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

We can then calculate n(A∩B) as:

$\begin{gathered} n(A\cup B)=n(A)+n(B)-n(A\cap B) \\ n(A\cap B)=n(A)+n(B)-n(A\cup B) \\ n(A\cap B)=288+183-434 \\ n(A\cap B)=37 \end{gathered}$

Answer: 37 [Option a]