Question

In a survey of $400$ students in a school, $100$ were listed as taking apple juice. $150$ as taking orange juice and $75$ were listed as taking both apple as well as orange juice. Find how many students were taking neither apple nor orange juice.

Answer 1

Let U=U= set of surveyed students
A=A= set of students taking apple juice.
B=B= set of students taking orange juice
Then n(U)=400;n(A)=100;n(B)=150;n(U)=400;n(A)=100;n(B)=150;
and n(A∩B)=75n(A∩B)=75
Now n(A′∩B′)=n(A∪B)′n(A′∩B′)=n(A∪B)′
=n(U)−n(A∪B)=n(U)−n(A∪B)
=n(U)−n(A)−n(B)+n(A∩S)=n(U)−n(A)−n(B)+n(A∩S)
=400−100−150+75=225=400−100−150+75=225
∴255∴255 students were taking neither apple juice nor orange juice.