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?

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.
n(U) = 600, n(T) = 150, n(C) = 225, n(T∩C) = 100
Where n(T∩C) means the number of students who take both tea and coffee.
To find: Number of students taking neither tea nor coffee i.e., we have to find n(T'∩C').
n(T'∩C') = n(T∪C)' [From De Morgan's law]
= n(U) - n(T∪C)
Where n(T∪C) is the number of students who take either tea or coffee.
= n(U) - [n(T) + n(C) - n(T∩C)]
= 600 - [150 + 225 - 100] [Substituting given values]
= 600 - 375
= 325
Hence, 325 students were taking neither tea nor coffee.