Question

20 teachers of a school either teach Mathematics or Physics. 12 of them teach Mathematics while 4 teach both the subjects. Then, the number of teachers teaching Physics only is

(a) 12

(b) 8

(c) 16

(d) 20

Answer 1

Let $n(P \cup M)=20, n(M)=12$ and $n(P \cap M)=4$

$n(P \cup M)$=$n(P)+n(M)-n(P \cap M)$

$20$=$n(P)+12-4 \Rightarrow n(P)$=12

$\therefore$ Only Physics teacher $=n(P)-n(A \cap B)=12-4=8$

So, The correct option of this question will be (b).