Out of a group of 20 teachers in a school, 10 teach Mathematics ,9 teach Physics and 7 teach Chemistry. 4 teach Mathematics and Physics but none teach  both Mathematics and Chemistry . How many teach Chemistry and Physics ? How many teach only Physics ?

The given information can be shown with the help of Venn diagram as follows :

It is given that :

 n (M) = 10

 n (P) = 9

 n (C) = 7

Also,  n (M∩P) = 4

 So,  the number of teacher who teaches Maths only  =  10 – 4  =  6

Since,  no teacher teach both Mathematics and Chemistry.

 ∴  There is nothing common in all the three.

Let  x  teachers teaches Physics  and  Chemistry.

 ∴  No. of teachers who teaches Physics only  =  5 – x

and No. of teachers who teaches Chemistry only =  7 – x

According to question –

 ∴   Two teachers teaches  Physics  and Chemistry.

and  5 – 2 =  3  teaches  Physics only.