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 A be the number of teachers who teach mathematics & B be the number of teachers who teach physics.

$$\begin{gathered} \mathrm{Given}: \\ n\left(A\right)=12 \\ n\left(A\cup B\right)=20 \\ n\left(A\cap B\right)=4 \\ \mathrm{To}\mathrm{find}: \\ n\left(B\right) \\ \mathrm{We}\mathrm{know}: \\ n\left(A\cup B\right)=n\left(A\right)+n\left(B\right)-n\left(A\cap B\right) \\ \Rightarrow 20=12+n\left(B\right)-4 \\ \Rightarrow n\left(B\right)=20-8=12 \\ \mathrm{Therefore},12\mathrm{teachers}\mathrm{teach}\mathrm{physics}. \end{gathered}$$