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

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.