Question - Determining the Number of Teachers Teaching Physics

Let $P$ be the number of teachers who teach physics and $M$ be the number of teachers who teach mathematics.

We are given that there are 20 teachers in total, of which 12 teach mathematics, 4 teach both physics and mathematics. We need to find how many teach physics.

We can use the principle of inclusion and exclusion to find the number of teachers who teach only physics.

Number of teachers teaching only mathematics is $M - 4$.

Number of teachers teaching physics, including those who teach both subjects, is $P$.

The sum of teachers teaching only mathematics, only physics, and both is the total number of teachers:

$(M - 4) + P = 20$

Given that $M = 12$, we substitute this into the equation:

$(12 - 4) + P = 20$

$8 + P = 20$

$P = 20 - 8$

$P = 12$

There are 12 teachers who teach physics.