Question

There are 200 individuals with a skin disorder of these, 120 had been exposed to the chemical $C_1, 50$ to chemical $C_2$ and 30 to both the chemicals $C_1$ and $C_2$.
The number of individuals exposed to chemical $C_1$ but not chemical $C_2$ is

• A. 90
• B. 80
• C. 150
• D. 120

Answer 1

Answer: (A)

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, $n(U)=200, n(A)=120, n(B)=50$ and $n(A \cap B)=30$

From the Venn diagram, we have
$A= (A-B) \cup(A \cap B)$
$n(A)= n(A-B)+n(A \cap B)$
( 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 .