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?

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 T and C is the set of students who take tea and coffee respectively.
n(T) = 150, n(C) = 225, n(T ∩ C) = 100
Use formula
n ( T ∪ C ) = n ( T ) + n ( C ) – n ( T ∩ C)
Plug the values we get,
= [150 + 225 - 100]
⇒ 275
Students taking neither tea nor coffee
⇒ Total students - student taking tea or coffee
⇒600 – 275
⇒ 325
Hence, 325 students were taking neither tea nor coffee.