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Standard IX

Mathematics

Venn Diagram

Chemical C1...

Question

Chemical $C_{1}$ but not chemical $C_{2}$

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Solution

Let $U =$ set of individuals suffering from the skin disorder
$A =$ set of individuals exposed to the chemical $C_{1}$
$B =$ set of individual exposed to the chemical $C_{2}$
Then $n (u) = 200, n (A) = 120, n (B) = 50$ and $n (A \cap B) = 30$
From the Venn diagram, we have
$A = (A - B) \cup (A \cap B)$
$∴ n (A) = n (A - B) + n (A \cap B)$
$A - B$ and $A \cap B$ are disjoint
$∴ n (A - B) = n (A) - n (A \cap B)$
$= 120 - 30 = 90$
Hence, $90$ individuals exposed t chemical $C_{1}$ but not to chemical $C_{2}$

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Chemical C1 but not chemical C2

Chemical $C_{1}$ but not chemical $C_{2}$