Question

If $n(A \cap B^C) = 5 , n(B \cap A^C) = 6, n(A \cap B) = 4$ then the value of $n\left(A \cup B\right)$ is

• A. 18
• B. 15
• C. 16
• D. 17

Answer 1

Answer: (B)

$n\left(A\cap B^{C}\right) =5, n\left(B\cap A^{C}\right) =6$
$ n\left(A\cap B\right)=4 $
$n\left(A\right) =n\left(A \cap B\right) +n\left(A\cap B^{C}\right) =4+5=9$
$ n\left(B\right) =n\left(A\cap B\right) +n\left(B\cap A^{C}\right) =6+4=10$
$ n\left(A\cup B\right)=n\left(A\right)+n\left(B\right)-n\left(A\cap B\right)$
$=9+10-4=15 $