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Sagot :
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
[tex]n(A)=14[/tex]
[tex]n(B)=11[/tex]
[tex]n(A\cup B)=20[/tex]
We know that,
[tex]n(A\cup B)=n(A)+n(B)-n(A\cap B)[/tex]
[tex]20=14+11-n(A\cap B)[/tex]
[tex]20=25-n(A\cap B)[/tex]
Subtract both sides by 25.
[tex]20-25=-n(A\cap B)[/tex]
[tex]-5=-n(A\cap B)[/tex]
[tex]5=n(A\cap B)[/tex]
We need to find the number of people who have a school certificate only, i.e. [tex]n(A\cap B')[/tex].
[tex]n(A\cap B')=n(A)-n(A\cap B)[/tex]
[tex]n(A\cap B')=14-5[/tex]
[tex]n(A\cap B')=9[/tex]
Therefore, 9 people have a school certificate only.
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