20 teachers of a school either teach mathematics or physics 12 of them mathematics white 4 teach both the subjects . The number of teachers teching 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.`