60 વ્યક્તિઓના સર્વેક્ષણમાં, 25 વ્યક્તિઓ સમાચા | vedclass

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Question

Let $A$ be the set of people who read newspaper $H.$

Let $B$ be the of people who read newspaper $T.$

Let $C$ be the set of people who read news

Vedclass · Accepted Answer

$30$

Vedclass · Answer

Let $A$ be the set of people who read newspaper $H.$

Let $B$ be the of people who read newspaper $T.$

Let $C$ be the set of people who read newspaper $I.$

Accordingly, $n(A)=25, n(B)=26,$ and $n(C)=26$

$n(A \cap C)=9, n(A \cap B)=11,$ and $n(B \cap C)=8$

$n(A \cap B \cap C)=3$

Let $U$ be the set of people who took part in the survey.

Let $a$ be the number of people who read newspapers $H$ and $T$ only.

Let $b$ denote the number of people who read newspapers $I$ and $H$ only.

Let $c$ denote the number of people who read newspapers $T$ and $I$ only.

Let $d$ denote the number of people who read all three newspapers.

Accordingly, $d=n(A \cap B \cap C)=3$

Now, $n(A \cap B)=a+d$

$n(B \cap C)=c+d$

$n(B \cap C)=c+d$

$n(C \cap A)=b+d$

$	herefore a+d+c+d+b+d=11+8+9=28$

$\Rightarrow a+b+c+d=28-2 d=28-6=22$

Hence, $(52-22)=30$ people read exactly one newspaper.

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