# There are 200 individuals with a skin disorder, 120 had been exposed to the chemical C1, 50 to chemical C2, and 30 to both the chemicals C1 and C2. Find the number of individuals exposed to(i) Chemical C1 but not chemical C2(ii) Chemical C2 but not chemical C1(iii) Chemical C1 or chemical C2

Given:

Total number of individuals with skin disorder = 200

Individuals exposed to chemical C1 = 120

Individuals exposed to chemical C2 = 50

Individuals exposed to chemicals C1 and C2 both = 30

To Find:

(i) Individuals exposed to Chemical C1 but not C2

Let us consider,

Total number of individuals with skin disorder = n(C) = 200

Individuals exposed to chemical C1 = n(C1) = 120

Individuals exposed to chemical C2 = n(C2) = 50

Individuals exposed to chemicals C1 and C2 both = n(C1 C2) = 30

Individuals exposed to Chemical C1 but not C2 = n(C1 - C2)

Venn diagram:

Now,

n(C1 - C2) = n(C1) – n(C1 C2)

= 120 – 30

= 90

Therefore, number of individuals exposed to chemical C � �1 but not C2 = 90

(ii) Individuals exposed to Chemical C2 but not C1

Let us consider number of Individuals exposed to Chemical C2 but not C1 = n(C2 – C1)

Now,

n(C2 – C1) = n(C2) – n(C1 C2)

= 50 – 30

= 20

Therefore, number of individuals exposed to chemical C � �2 but not C1 = 20

(iii) Individuals exposed to Chemical C1 or chemical C2

Let us consider number of Individuals exposed to Chemical C1 or chemical C2 = n(C1 C2)

Now,

n(C1 C2) = n(C1) + n(C2) - n(C1 C2)

= 120 + 50 – 30

= 140

Therefore, number of individuals exposed to chemical C � �1 or C2 = 140

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RS Aggarwal - Mathematics