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.
$n(U)=600,n(T)=150,n(C)=225,n(T\cap C)=100$
To find: Number of student taking neither tea nor coffee i.e., we have to find $n(T^{\prime }\cap C^{\prime })$.
$n(T^{\prime }\cap C^{\prime })=n(T\cup C{)}^{\prime }$
$=n(U)-n(T\cup C)$
$=n(U)-[n(T)+n(C)-n(T\cap C)]$
$=600-[150+225-100]$
$=600-275$
$=325$
Hence, 325 students were taking neither tea nor coffee.