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 $C _{1}$ but not chemical $C _{2}$
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 $C _{1}$ but not chemical $C _{2}$
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 Venn diagram given in Fig we have $A=(A-B) \cup(A \cap B)$
$n(A) = n(A - B) + n(A \cap B)\quad $ ( Since $(A - B)$ and $A \cap B$ are disjoint. )
or $n( A - B )=n( A )-n( A \cap B )=120-30=90$
Hence, the number of individuals exposed to chemical $C_{1}$ but not to chemical $C_{2}$ is $90$
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