Question

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 1

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.

Accordingly, n(U) = 600, n(T) = 150, n(C) = 225, n(T ∩ C) = 100 To find:

Number of student taking neither tea nor coffee i.e.,

we have to find n(T' ∩ C').

n(T' ∩ C') = n(T ∪ C)'

 = n(U) – n(T ∪ C)

= n(U) – [n(T) + n(C) – n(T ∩ C)]  

11 = 600 – [150 + 225 – 100] = 600 – 275 = 325

Hence,

325 students were taking neither tea nor coffee.