In a class of 40 students, 24 like to play guitar and 25 like to play piano. If each students like at least one of the musical instrutment, then how many like to play both piano and guitar?

Explanation

Let G be the set of students who like to play guitar
Let P be the set of students who like to play plano
Let `(G cup P)` be the set of students who like to play at least one musical instrument.
`(G cap P)` is the set of students who like to play both
Given: `n(G)=24, n(P)=25, n(G cup P)=40`
`n(G capP)=?`
Using the formula
`n(G cup P)=n(G)+n(P)-n(G cap P)`
`Rightarrow 40=24+25-n(G cap P)`
`Rightarrown(G cap P)=49-40`
`therefore n(G cap P)=9`
Thus, 9 students like to play both guitar and piano.