Question

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

Answer 1

Given data:
Number of teachers who teach Mathematics of Physics $=n(M\cup P)=20$
Number of teachers who teach Mathematics $=n\left(M\right)=12$
Number of teachers who teach both Mathematics and Physics $=n(M\cap P)=4$

Solve for number of teachers who teach physics.
$n(M\cup P)=n\left(M\right)+n\left(P\right)-n(M\cap P)$
$\Rightarrow 20=12+n\left(P\right)-4$
$\Rightarrow n\left(P\right)=20-8$
$\Rightarrow n\left(P\right)=12$

Final answer:
Hence, $12$ teachers teach Physics.