Determining the Number of Teachers Teaching Physics
<p>Let $P$ be the number of teachers who teach physics and $M$ be the number of teachers who teach mathematics.</p>
<p>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.</p>
<p>We can use the principle of inclusion and exclusion to find the number of teachers who teach only physics.</p>
<p>Number of teachers teaching only mathematics is $M - 4$.</p>
<p>Number of teachers teaching physics, including those who teach both subjects, is $P$.</p>
<p>The sum of teachers teaching only mathematics, only physics, and both is the total number of teachers:</p>
<p>$(M - 4) + P = 20$</p>
<p>Given that $M = 12$, we substitute this into the equation:</p>
<p>$(12 - 4) + P = 20$</p>
<p>$8 + P = 20$</p>
<p>$P = 20 - 8$</p>
<p>$P = 12$</p>
<p>There are 12 teachers who teach physics.</p>
