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

A

$90$

B

$90$

C

$90$

D

$90$

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 Venn diagram given in Fig we have $A=(A-B) \cup(A \cap B)$

$n(A) = n(A – B) + n(A \cap B)\quad $ ( Since $(A – B)$ and $A \cap B$ are disjoint. )

or $n( A – B )=n( A )-n( A \cap B )=120-30=90$

Hence, the number of individuals exposed to chemical $C_{1}$ but not to chemical $C_{2}$ is $90$

Standard 11
Mathematics

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