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in Mathematics by (52.5k points)

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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Best answer

Let U = set of students in a school.

A = set of students taking tea

B = set of students taking coffee

Then n(∪) = 600; n(A) = 150; n(B) = 225; n(A∩B) = 100 

∴ n(Au B) = n(A) + n(B)-n(A∩B) = 150 + 225-100 =275 

Now n(A’∩B’) = n(A∪B) 

= n(∪)-n(A∪5) = 600-275 = 325 

∴ 325 students were taking neither tea nor coffee.

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