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.