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

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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 mathematics or physics = n(M ∪ P ) = 20 Number of teachers who teach mathematics = n(M) = 12 & Number of teachers who teach mathematics 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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