Question

Of the 36 students in a certain class, 10 are in the chess club and 13 are in the bridge club. If 20 of the students are not in either club, how many of the students are in only one of the two clubs?

Answer 1

Total 9 students are in only one of the two clubs.

Explanation:

A : Student in the chess club.

B : Student in bridge club.

Total number of students, S=36

Total students in chess club, n(A)=10

Total students in bridge club, n(B)=13

Students are not in either club
`n(A\cup B)'=20`

Number of students are in either chess club or bridge club is

`n(A\cup B)=S-n(A\cup B)'=36-20=16`

Total number of student in both clubs.

`n(A\cap B)=n(A)+n(B)-n(A\cup B)=10+13-16=7`

Students only in chess club,

`n(A\cap B')=n(A)-n(A\cap B)=10-7=3`

Students only in bridge club,

`n(A'\cap B)=n(B)-n(A\cap B)=13-7=6`

Total students that are in only one of the two clubs,

`T=3+6=9`

Therefore, total 9 students are in only one of the two clubs.