Question

In a survey of 25 students, it was found that 15 had taken mathematics, 12 had taken physics and 11 had taken chemistry, 5 had taken mathematics and chemistry, 9 had taken mathematics and physics, 4 had taken physics and chemistry and 3 had taken all the three subjects.

Find the number of students that had taken physics and chemistry but not mathematics.

• A. $1$
• B. $2$
• C. $3$
• D. $10$

Answer 1

The correct option is A $1$

Let $M=$ Set of student who taken Mathematics only

$C=$ Set of student who taken chemistry only.

$P=$ Set of student who taken Physics only.

$\therefore n\left(M\right)=15,n\left(P\right)=12,n\left(C\right)=11,n(M\cap C)=5,n(M\cap P)=9,n(P\cap C)=4,n(M\cap P\cap C)=3$

The number of student that had taken Physics and Chemistry but not Mathematics.

$\Rightarrow n\left(\right(P\cap C)-M)$

$\Rightarrow n(P\cap C)-n(P\cap C\cap M)=4-3=1$