In Class XI of a certain school, there are 30 students in a Mathematics class and 20 students in Biolog class. Find the number of students which are in Mathematics class or in Biology class in the following cases:
(i) Two classes are conducted at the same time.
(ii) Two classes are condcuted at different time and 5 students study both the subject

Explanation

Let M be the set of students in Mathematics class.
Let B be the set of students in Biology class
(i) n(M)=30, n(B)=20
`M cap B=phi` `(therefore` Both classes conducted at same time, no student an attend both classes).
`M cap B=phi`
`n(M cap B)=n(M)+n(B)-n(M cap B)`
`Rightarrow n(M cup B)=30+20-0`
`therefore n(M cup B)=50`
`(ii) n(M cup B)=5 (given)`
`n(M cup B)=n(M)+n(B)-n(M cap B)`
`=30+20-5=45`