Answer:
There are 8 number of hairy dogs.
Step-by-step explanation:
It is given that:
Number of small dogs (Let it be [tex]n(A)[/tex]) = 9
To find:
Number of hairy dogs (Let it be [tex]n(B)[/tex]) = ?
Also given the following things:
Number of hairy or small dogs ([tex]n(A \cup B)[/tex]) = 15
Number of hairy and small dogs(both) ([tex]n(A \cap B)[/tex]) = 2
We can use the following formula:
[tex]n(A \cup B) = n(A) + n(B) - n(A \cap B)[/tex]
To find [tex]n(A \cup B)[/tex], We have to subtract [tex]n(A \cap B)[/tex] once because [tex]n(A) \ and \ n(B)[/tex] both contain the common part and it gets added twice. So, it is subtracted once.
Putting the values in above formula:
[tex]\Rightarrow 15 = 9 + n(B) - 2\\\Rightarrow n(B) = 15 - 7\\\Rightarrow n(B) = 8[/tex]
Hence, the number of hairy dogs are 8.
