Question

There are 200 individuals with a skin disorder, 120 has been exposed to 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

(i) chemical $C_1$ or chemical $C_2$.

(ii) chemical $C_1$ but not chemical $C_2$.

(iii) chemical $C_2$ but not chemical $C_1$.

Answer 1

Let U denotes the universal set consisting of individuals suffering from the skin disorder. A denotes the set of individuals exposed to chemical $C_1$, and B denotes the set of individuals exposed to chemical $C_2$.

We have,

n (U) = 200, n (A) =120, n (B) = 50

and n(A $\cap$ B)= 30

(i) Number of individuals exposed to chemical $C_1$ or chemical $C_2$,

$n(A\cup B)=n\left(A\right)+n\left(B\right)-n(A\cap B)$

= 120 + 50 - 30 = 140

(ii) Number of individuals exposed to chemical $C_1$, but not chemical $C_2$,

$n(A\cap B^{\prime })=n\left(A\right)-n(A\cap B)$

= 120 - 30 = 90

(iii) Number of individuals exposed to chemical $C_2$ but not chemical $C_1$.

$n(A^{\prime }\cap B)=n\left(B\right)-n(A\cap B)$

= 50 - 30 =20