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In a survey of 600 students in a scho...

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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Let universal set U is the set of all students of the survey and T is the set of student taking tea and C is the set of students taking coffee
then `n(U)=600,n(T)=150,n(C)=225`
and `n(T capC)=100`
`:. n(T cup C)-n(T)+n(C)-n(T cap C)`
`150 + 225 - 100`
`= 275`
Number of students who take neither tea nor coffee
`= n(U)-n(T cup C)`
`= 600-275 = 325`
Therefore, 325 students take neither tea nor coffee.
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