Question

In a school, there are 20 teachers who teach Mathematics or Physics. Of these, 12 teach Mathematics and 4 teach both Physics and Mathematics. Then, number of teachers who teach Physics, is

• A. 28
• B. 12
• C. 4
• D. 36

Answer 1

Answer: (B)

Let $M$ denote the set of teachers who teach Mathematics and $P$ denote the set of teachers who teach Physics. In the statement of the problem, the word 'or' gives us a clue of union and the word 'and' gives us a clue of intersection. We have,
$n(M \cup P)=20, n(M)=12 $
and $ n(M \cap P)=4$
We wish to determine $n(P)$.
Using the result
$n(M \cup P) =n(M)+n(P)-n(M \cap P), $ we obtain
$20 =12+n(P)-1$
Thus, $ n(P)=12$
Hence, 12 teachers teach Physics.