Question

There are $200$ individuals with a dermatological disorder. $120$ were exposed to the chemical $C1$, $50$ to chemical $C2$, and $30$ to both the chemicals $C1$ and $C2$. What is the number of individuals exposed to?
(i) chemical $C1$ but not chemical $C2$
(ii) chemical $C2$ but not chemical $C1$
(iii) chemical $C1$ or chemical $C2$
$\left[2\right]$

Answer 1

A signifies the set of individuals exposed to the chemical $C1$, while B denotes the set of individuals exposed to the chemical $C2$
$n\left(U\right)=200$,
$n\left(A\right)=120$,
$n\left(B\right)=50$,
$n(A\cap B)=30$

(i) $n(A-B)=n\left(A\right)-n(A\cap B)=120-30=90$
$\left[0.5\right]$
(ii) $n(B-A)=n\left(B\right)-n(A\cap B)=50-30=20$
$\left[0.5\right]$
(iii) $n(A\cup B)=n\left(A\right)+n\left(B\right)-n(A\cap B)=120+50-30=140$
$\left[1\right]$