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In a school there are 25 teachers who teach engineering or management. Of these, 15 teach engineering and 6 teach both engineering and management. How many teach management?
Solution
Let M be the set of teachers who teach management and E be the set of teachers who teach engineering. Here ‘or’ means union and ‘and’ means intersection. So, we have
n ( E ∪ M ) = 25 , n ( E ) = 15 and n ( E ∩ M ) = 6
We have to calculate n ( M ).
According to formula
n ( E ∪ M ) = n ( E ) + n ( M ) – n ( E∩ M ),
We obtain
25 = 15 + n ( M ) – 6
Thus n ( M ) = 16
Hence 16 teachers teach management.
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