Question

In a group of $40$ student, $26$ student like orange but not banana, while $32$ student like orange. If all the student like at least one of the two fruits, find the number of student who like (i) both orange and banana (ii) only banana. Draw a venn diagram to represent the given data.

Answer 1

Let us assume $\xi$ be the total students Let us assume $P$ be the students who like orangeAnd also assume that $Q$ be the students who like banana From the question it is given that, $n\left(\xi \right)=40$
$n(P-Q)=26$
$n\left(Q\right)=32$
$n(P\cup Q)=40$
Then,(i) Total number of students like both orange and banana. i.e.
$n(P\cap Q)=6$
(ii) Number of students like only banana $=40-32=8$