Correct Answer - Option 2 : 7
Concept:
Let A and B denote two sets of elements.
- n(A) and n(B) are the number of elements present in set A and B respectively.
- n(A ⋃ B) is the total number of elements present in either set A or B.
- n(A ⋂ B) is the number of elements present in both the sets A and B.
-
n(A ⋃ B) = n(A) + n(B) - n(A ⋂ B).
Calculation:
Let A be the set of teachers who teach Mathematics and B be the set of those who teach Physics.
It is given that n(A ⋃ B) = 35, n(A) = 23 and n(B) = 19.
By using the relation n(A ⋃ B) = n(A) + n(B) - n(A ⋂ B), we get:
35 = 23 + 19 - n(A ⋂ B)
⇒ n(A ⋂ B) = 42 - 35 = 7.
∴ The number of teachers who teach both the subjects is 7.