Question

In a school with an enrolment of $950$ students, each student must join either the lions club or the country club or both. Given that $646$ students are members of the lions club and $532$ are members of the country club, calculate the number of students who are members of both clubs.

Answer 1

Let A and B denote the set of students who are members of lions club and country club respectively.

$n\left(A\right)=646$

$n\left(B\right)=532$

$n(A\cup B)=950$

$n(A\cup B)=n\left(A\right)+n\left(B\right)-n(A\cap B)$

$\therefore n(A\cap B)=n\left(A\right)+n\left(B\right)-n(A\cup B)$

$=646+532-950=228$

Hence, $228$ students are members of both the clubs.