Question

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

• A. 9
• B. 17
• C. 5
• D. 10

Answer 1

The correct option is A 9

Let G be the set of students who like to play guitar and P be the set of students who like to play piano.
Then, (G∪P) be the set of students who like play at least one musical instrument:

n(G) = 24, n(P) = 25, n(G∪P) = 40
n(G∪P) = n(G) + n(P) – n(G∩P)
⇒ 40 = 24 + 25 – n (G∩P)
⇒ 40 = 49 – n(G∩P)
⇒ n(G∩P) = 49 – 40
∴ n(G∩P) = 9

So, option a is correct.