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Example 24 - In a school, 20 teachers teach maths or physics

Example 24 - Chapter 1 Class 11 Sets - Part 2

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Example 24 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 teach physics ? Let M denote the set of teachers who teach mathematics and P denote the set of teachers who teach physics. The word ‘or’ means union and the word ‘and’ means intersection. Hence, Number of teachers who teach Maths or Physics = n(M ∪ P) = 20 Number of teachers who teach Maths = n(M) = 12 Number of teachers who teach Maths and physics = n(M ∩ P) = 4 Number of teachers who teach physics = n(P) = ? We know that n (M ∪ P) = n(M) + n(P) – n (M ∩ P), 20 = 12 + n(P) – 4 20 = 12 + n(P) – 4 20 = 8 + n(P) Thus n(P) = 12. Hence, 12 teachers teach physics.

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.