1.Set Theory
medium

$200$ व्यक्ति किसी चर्म रोग से पीड़ित हैं, इनमें $120$ व्यक्ति रसायन $C _{1}, 50$ व्यक्ति रसायन $C _{2}$, और $30$ व्यक्ति रसायन $C _{1}$ और $C _{2}$ दोनों ही से प्रभावित हुए हैं, तो ऐसे व्यक्तियों की संख्या ज्ञात कीजिए जो प्रभावित हुए हों

रसायन $C _{2}$ किंतु रसायन $C _{1}$ से नहीं,

A

$20$

B

$20$

C

$20$

D

$20$

Solution

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 $20 .$

Standard 11
Mathematics

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