Given:
[tex]n(A)=12[/tex]
[tex]n(B)=7[/tex]
[tex]n(A\cup B)=10[/tex]
To find:
The value of [tex]n(A\cap B)[/tex].
Solution:
We know that,
[tex]n(A\cup B)=n(A)+n(B)-n(A\cap B)[/tex]
After substituting the given values, we get
[tex]10=12+7-n(A\cap B)[/tex]
[tex]10+n(A\cap B)=19[/tex]
[tex]n(A\cap B)=19-10[/tex]
[tex]n(A\cap B)=9[/tex]
Therefore, the value of [tex]n(A\cap B)[/tex] is 9.
Note: The values are not correct because [tex]n(A)[/tex] cannot be greater than [tex]A\cup B[/tex]. The steps of solving these types of question are shown above.
