20 teachers of a school either teach Mathematics or Physics. 12 of them teach Mathematics while 4 teach both the subjects. The number of teachers teaching Physics only, is _____.
Answer & explanation
Let M = Set of teachers teaching Mathematics.
P = Set of teachers teaching Physics.
We have,
$n(M∪P)=20,\,n(m)=12$ and $n(M∩P)=4$
$∴n(M∪P)=n(m)+n(P)-n(M∩P)$
$⇒20+12+n(P)-4$
$⇒n(P)=12$
So, the required number = $n(P)-n(M∩P)=12-4=8$