# 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?

Given :

20 teachers teach physics or math.

4 teachers teach physics and math.

12 teach maths

Let us denote teachers who teach physics as n(P) and for Maths n(M).

Now ,

20 teachers teach physics or math = n(P M) = 20

4 teachers teach physics and math = n (P M) = 4

12 teach maths = n(M) =12

We know,

n (P M) = n(M) + n(P) – n (P M)

Substituting the values we get

20 = 12+n(P)–4

20 = 8+ n(P)

n(P) =12

There are 12 physics teachers.

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