# In a school, all

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

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