`20` teachers of a school either teach mathematics or physics `12` of them mathematics while `4` teach both the subjects . The number of teachers teaching physics only ,is

Options

A. `12`
B. `8`
C. `16`
D. none of these

Answer

B

Explanation

Let M - set of teachers teching Mathematices p= set of techers teching physics .
we have ,
`n(Mcup P) = 20,n(m) = 12 n (M cup P)=4`
`therefore n(Mcup P) =n(M) +n(P) -N(Mcap P)`
`implies 20=12+n(p)-4`
`implies n(p) =12`
so the required number `=n(P) -n(McupP) =12-4=8.`