Question

20 people applied for a job. Everyone either has a school certificate or diploma or even both. If 14 have school certificates and 11 diplomas how many have a school certificate only

Answer 1

Given:

Either has a school certificate or diploma or even both = 20 people

Having school certificates = 14

Having diplomas = 11

To find:

The number of people who have a school certificate only.

Solution:

Let A be the set of people who have school certificates and B be the set of people who have diplomas.

According to the given information, we have

`n(A)=14`

`n(B)=11`

`n(A\cup B)=20`

We know that,

`n(A\cup B)=n(A)+n(B)-n(A\cap B)`

`20=14+11-n(A\cap B)`

`20=25-n(A\cap B)`

Subtract both sides by 25.

`20-25=-n(A\cap B)`

`-5=-n(A\cap B)`

`5=n(A\cap B)`

We need to find the number of people who have a school certificate only, i.e.
`n(A\cap B')`.

`n(A\cap B')=n(A)-n(A\cap B)`

`n(A\cap B')=14-5`

`n(A\cap B')=9`

Therefore, 9 people have a school certificate only.