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
Correct answer: option 3
The correct answer is Option (3) → 8
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 = $n (P)-n (M∩P) = 12-4 = 8$