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Answer the following: In a school there are 20 teachers who teach Mathematics or Physics. Of these, 12 teach Mathematics and 4 teach both Physics and Mathematics. How many teachers teach Physics? - Mathematics and Statistics

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Question

Answer the following:

In a school there are 20 teachers who teach Mathematics or Physics. Of these, 12 teach Mathematics and 4 teach both Physics and Mathematics. How many teachers teach Physics?

Diagram
Sum
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Solution

Let A = set of teachers who teach Mathematics

B = set of teachers who teach Physics

∴ n(A ∪ B) = 20, n(A) = 12, n(A ∩ B) = 4

Since, n(A ∪ B) = n(A) + n(B) – n(A ∩ B)

∴ 20 = 12 + n(B) – 4

∴ n(B) = 12

∴ Number of teachers who teach physics = 12

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Chapter 5: Sets and Relations - Miscellaneous Exercise 5.2 [Page 105]

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Balbharati Mathematics and Statistics 2 (Arts and Science) [English] Standard 11 Maharashtra State Board
Chapter 5 Sets and Relations
Miscellaneous Exercise 5.2 | Q II. (4) | Page 105

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