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There are 35 teachers in a school, who teach either Mathematics or Physics. Of these, 23 teach Mathematics and 19 teach Physics. How many teach both Mathematics and Physics?

There are 35 teachers in a school, who teach either Mathematics or Physics. Of these, 23 teach Mathematics and 19 teach Physics. How many teach both Mathematics and Physics? Correct Answer 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).

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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.

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