In a survey of 600 students in a school. 150 students were found to be

1.	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?
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.

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?

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.