Answer:
[tex]\boxed{n(A) = 20}[/tex]
Step-by-step explanation:
We know
[tex]n(B)= 12[/tex]
From [tex]n(A \cap B)=9[/tex] and [tex]n(A \cup B)=23[/tex], we conclude [tex]n(A \cup B)=23 = n(A \cap B) + n(A- B) + n(B- A)[/tex]
Once [tex]n(B)= 12[/tex], then [tex]n(B- A) = 12-9 = \boxed{3}[/tex]
Taking
[tex]23 = n(A \cap B) + n(A- B) + n(B- A) = 9+ n(A- B) +3 = \boxed{12+ n(A- B) }[/tex]
Therefore,
[tex]n(A- B) =11 \implies n(A) - 9 = 11 \implies \boxed{n(A) = 20}[/tex]
