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?
Solution:
Let A be the number of teachers who teach mathematics & B be the number of teachers who teach physics.
Given :
$n(A)=12$
$n(A \cup B)=20$
$n(A \cap B)=4$
To find:
$n(B)$
We know:
$n(A \cup B)=n(A)+n(B)-n(A \cap B)$
$\Rightarrow 20=12+n(B)-4$
$\Rightarrow n(B)=20-8=12$
Therefore, 12 teachers teach physics.