Question

If n(A u B)=23, n(A n B)=9,and n(B)=12. find n(A)

Answer 1

Answer:

$\boxed{n(A) = 20}$

Step-by-step explanation:

We know

$n(B)= 12$

From $n(A \cap B)=9$  and $n(A \cup B)=23$, we conclude  $n(A \cup B)=23 = n(A \cap B) + n(A- B) + n(B- A)$

Once  $n(B)= 12$, then  $n(B- A) = 12-9 = \boxed{3}$

Taking

$23 = n(A \cap B) + n(A- B) + n(B- A) = 9+ n(A- B) +3 = \boxed{12+ n(A- B) }$

Therefore,

$n(A- B) =11 \implies n(A) - 9 = 11 \implies \boxed{n(A) = 20}$