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In a school there are 20 teachers who teach mathematics or physics, of there, 12 teach mathematics and 4 teach both physics and mathematics. How many teach only physics ?

In a school there are 20 teachers who teach mathematics or physics, of there, 12 teach mathematics and 4 teach both physics and mathematics. How many teach only physics ? Correct Answer 8

Given:

Number of teachers who teach mathematics or physics = n (M ∪ P) = 20

Number of teachers who teach mathematics = n (M) = 12

Number of teachers who teach both mathematics and physics = n (M ∩ P) = 4

Concept:

n (M ∪ P) = n (M) + n (P) - n (M ∩ P)

Calculation:

We need to find the number of teachers who teach physics i.e., n (P)

⇒ n (M ∪ P) = n (M) + n (P) - n (M ∩ P)

⇒ 20 = 12 + n (P) - 4

⇒ n (P) = 12

Number of teachers who teaches only physics = 12 - 4 = 8

Hence, the number of teachers who teach physics is 8.

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