In a survey of 600 students in a school,150 s | vedclass

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(A) Let $U$ be the set of all students who took part in the survey.Let $T$ be the set of students taking tea.Let $C$ be the set of students taking cof

Vedclass · Accepted Answer

$325$

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(A) Let $U$ be the set of all students who took part in the survey.Let $T$ be the set of students taking tea.Let $C$ be the set of students taking coffee.Given: $n(U) = 600, n(T) = 150, n(C) = 225, n(T \cap C) = 100$.We need to find the number of students taking neither tea nor coffee,which is $n(T' \cap C')$.Using De Morgan's Law,$n(T' \cap C') = n(T \cup C)' = n(U) - n(T \cup C)$.First,find $n(T \cup C) = n(T) + n(C) - n(T \cap C) = 150 + 225 - 100 = 275$.Now,$n(T' \cap C') = 600 - 275 = 325$.Thus,$325$ students were taking neither tea nor coffee.

In a survey of $600$ students in a school,$150$ students were found to be taking tea and $225$ taking coffee,$100$ were taking both tea and coffee. Find how many students were taking neither tea nor coffee?

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