Question

In a school there are 20 teachers who teach mathematics or physics. Of these, 12 teach mathematics and 4 teach physics and mathematics. How many teach physics ?

Answer 1

Let n (P) denote the number of teachers who teach Physics and n (Q) denote the number of teachers who teach Mathematics.

We have,

n (P or M) = 20

i.e. n (P $\cup$ M) = 20

n (M) = 12

and $n(P\cap M)=4$

To find : n (P)

We know $n(P\cup M)=n\left(P\right)+n\left(M\right)-n(P\cap M)$

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

$\Rightarrow 20=n\left(P\right)+8$

$\Rightarrow n\left(P\right)=20-8$

= 12

$\therefore$ There are 12 Physics teacher.