Question

In a survey of students it was found that $50$ students are studying Physics, $50$ Chemistry and $50$ are studying Mathematics. But $10$ are studying all the three subjects, while $22$ are studying Physics and Chemistry, $20$ are studying Chemistry and Maths and $17$ are studying Physics and Maths. Calculate:

How many of them are studying Mathematics only?

Answer 1

R.E.F image

$A-$ no of students studying Physics

$B-$ no of students studying Chem

$C-$ no of students studying Maths

$A\cap B-$ no of students studying Phy of chem

$B\cap C-$ no of students studying Chem of math

$C\cap A-$ no of students studying maths of Phy

$A\cap B\cap C-$ no of students studying all '3' subjectively

(i) no of students in chem is $\cap \left(B\right)-\cap (A\cap B)-\cap (B\cap C)+\cap (A\cap B\cap C)$

$\Rightarrow 50-22-20+10=18$

(ii) no of students in Phy only $\cap \left(A\right)-\cap (A\cap B)-\cap (A\cap C)+\cap (A\cap B\cap C)$

$\Rightarrow 50-22-17+10=21$

(iii) no of students in maths only $-\cap \left(C\right)-\cap (B\cap C)=\cap (A\cap C)+\cap (A\cap B\cap C)$

$\Rightarrow 50-20-17+10=23$