In a school, all the students play either Foot ball or Volley ball or both. 300 students play Foot ball, 270 students play Volley ball and 120 students play both games. Find

Question

In a school, all the students play either Foot ball or Volley ball or both. 300 students play Foot ball, 270 students play Volley ball and 120 students play both games. Find
i. the number of students who play Foot ball only

ii. the number of students who play Volley ball only

iii. the total number of students in the school

Philoid · Accepted Answer

Let A denote the set of students who play football and B denote the set of students who play volleyball.

Then, n(A) = 300, n(B) = 270, n(A ∩ B) = 120.

i. Number of students who play volleyball only are represented by (A – B).

n(A–B) = n(A) – n(A ∩ B)

n(A–B) = 300 – 120 = 180

ii. Number of students who play volleyball only are represented by (B – A).

n(B–A) = n(B) – n(A ∩ B)

n(A–B) = 270 – 120 = 150

iii. Number of students in the school are represented by (A ∪ B)

We have, n(A ∪ B) = n(A) + n(B) – n(A ∩ B)

n(A ∪ B) = 300 + 270 – 120

n(A ∪ B) = 570 – 120 = 450