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There are $200$ individuals with a skin disorder, $120$ had been exposed to the chemical $C _{1}, 50$ to chemical $C _{2},$ and $30$ to both the chemicals $C _{1}$ and $C _{2} .$ Find the number of individuals exposed to
Chemical $C_{2}$ but not chemical $C_{1}$
$20$
$20$
$20$
$20$
Solution
Let $U$ denote the universal set consisting of individuals suffering from the skin disorder, $A$ denote the set of individuals exposed to the chemical $C_{1}$ and $B$ denote the set of individuals exposed to the chemical $C_{2}$
Here $\quad n( U )=200, n( A )=120, n( B )=50$ and $n( A \cap B )=30$
From the Fig we have
$B=(B-A) \cup(A \cap B)$
and so, $\quad n( B )=n( B – A )+n( A \cap B )$
( Since $B – A$ and $A \cap B$ are disjoint .)
or $n(B – A) = n(B) – n(A \cap B)$
$ = 50 – 30 = 20$
Thus, the number of individuals exposed to chemical $C_{2}$ and not to chemical $C_{1}$ is $20 .$
