Sets-Relations-And-Functions Question 152

Question: In a school, there are 20 teachers who teach mathematics of physics of these, 12 teach mathematics and 4 teach both math?s and physics then the number of teachers teaching only physics are

Options:

A) 4

B) 8

C) 12

D) 16

Show Answer

Answer:

Correct Answer: B

Solution:

  • [b]Let $ M= $ set of Mathematics teaches $ P= $ set of physics teachers n(only math?s teacher) $ =n(M)-n(M\cap P)=12-4=8 $ Also, $ n(M\cup P)=n $ (only math teachers) +n (only physics teachers) $ +n(M\cap P) $ $ 20=8+4+n $ (only physics teachers)
    $ \Rightarrow n=8. $