In a group of 65 people,40 like cricket and 1 | vedclass

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Question

(A) Let $C$ be the set of people who like cricket and $T$ be the set of people who like tennis.Given: $n(C \cup T) = 65$,$n(C) = 40$,and $n(C \cap T)

Vedclass · Accepted Answer

$25$ only tennis,$35$ total tennis

Vedclass · Answer

(A) Let $C$ be the set of people who like cricket and $T$ be the set of people who like tennis.Given: $n(C \cup T) = 65$,$n(C) = 40$,and $n(C \cap T) = 10$.Using the formula $n(C \cup T) = n(C) + n(T) - n(C \cap T)$:$65 = 40 + n(T) - 10$$65 = 30 + n(T)$$n(T) = 65 - 30 = 35$.So,the total number of people who like tennis is $35$.To find the number of people who like tennis only (not cricket),we calculate $n(T - C)$:$n(T - C) = n(T) - n(C \cap T)$$n(T - C) = 35 - 10 = 25$.Thus,$25$ people like only tennis and $35$ people like tennis in total.

In a group of $65$ people,$40$ like cricket and $10$ like both cricket and tennis. How many like tennis only and not cricket? How many like tennis?

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