What is a universal set explain it n also examples for it along with examples of union n intersection

Question

Arun · Answer

Universal Set – the set containing all objects or elements and of which all other sets are subsets.

Example

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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What is a universal set explain it n also examples for it along with examples of union n intersection

What is a universal set explain it n also examples for it along with examples of union n intersection

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