There are 200 individuals with a skin disorde | vedclass

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(A) Let $U$ denote the universal set consisting of individuals suffering from the skin disorder,$A$ denote the set of individuals exposed to the chemi

Vedclass · Accepted Answer

$90$

Vedclass · 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 $n(A \cap B) = 30$.We need to find the number of individuals exposed to chemical $C_{1}$ but not to chemical $C_{2}$,which is represented by $n(A - B)$.From the properties of sets,we have $A = (A - B) \cup (A \cap B)$.Since $(A - B)$ and $(A \cap B)$ are disjoint sets,we have:$n(A) = n(A - B) + n(A \cap B)$Substituting the given values:$120 = n(A - B) + 30$$n(A - B) = 120 - 30 = 90$Thus,the number of individuals exposed to chemical $C_{1}$ but not to chemical $C_{2}$ is $90$.

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 $C_{2}$.

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