Question

There are 60 students in a Mathematics class and 90 students in Physics class. Find the number of students which are either in Physics class or Mathematics class in the following cases.

(i) Two classes meet at the same hour.

(ii) Two classes meet at different hours and 30 students are enrolled in both the courses.

(iii) What value is shown here ?

Answer 1

Let M be the set of students in Mathematics class and P be the set of students in Physics class :

Given that, n(M) = 60 and n(P) = 90

(i) Two classes meet at same hour, i.e.

$M\cap P=\varphi \Rightarrow n(M\cap P)=0$ Now, $n(M\cup P)=n\left(M\right)+n\left(P\right)-n(M\cap P)$

= 60 + 90 - 0 = 150

(ii) In this case, two classes meet a different hours and 30 students are enrolled in both the courses.

$\therefore n(M\cup P=n(M)+n(P)-n(M\cap P)$

$60+90-30=120$

(iii) Most of the students study Physics in comparison of Mathematics.