There are 200 individuals with a skin disorde | vedclass

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Question

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

Vedclass · Accepted Answer

$20$

Vedclass · Answer

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 $20 .$

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 $C_{1}$

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