In a group of 40 students , 26 students take tea , 18 take coffee and 8 take neither tea nor coffee . How many take both tea and coffee?

Symbols used:-

U = Union

^ = Intersection

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Let the set of students taking tea be A, and coffee be B.

Therefore,

n(A U B) = 40 - 8 = 32

n(A) = 26

n(B) = 18

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By the formula:-

n(A U B) = n(A) + n(B) - n(A^B)

32 = 26 + 18 -n(A^B)

Hence, n(A^B) = 26 + 18 - 32 = 12.

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Hence 12 students take both tea and coffee.

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