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Question
In a school there are 20 teachers who teach athematics or physics. Of these, 12 teach mathematics and 4 teach physics and mathematics. How many teach physics?
Solution
Let A be the number of teachers who teach mathematics & B be the number of teachers who teach physics.
\[\text{ Given }: \]
\[n\left( A \right) = 12\]
\[n\left( A \cup B \right) = 20\]
\[n\left( A \cap B \right) = 4\]
\[\text{ To find }: \]
\[n\left( B \right)\]
\[\text{ We know }: \]
\[n\left( A \cup B \right) = n\left( A \right) + n\left( B \right) - n\left( A \cap B \right)\]
\[ \Rightarrow 20 = 12 + n\left( B \right) - 4\]
\[ \Rightarrow n\left( B \right) = 20 - 8 = 12\]
\[\text{ Therefore, 12 teachers teach physics } .\]
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