In a school there are 20 teachers who teach mathematics or physics.
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 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.

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