Jane sought the intersection of two sets, $A$ and $B$, defined by their characteristic properties. $$\begin{aligned} A&=\{x\in Z;x^2=9\}\cr B&=\{x\in Z;-4 < x < 3\} \end{aligned}$$
She solved the problem in the following steps:
(1) She wrote the set $A$ by listing its elements: $$A=\{3\}$$
(2) Similarly, she wrote the set $B$ by listing the elements: $$B=\{-4,-3,-2,-1,0,1,2,3\}$$
(3) Then, she determined the intersection: $$A\cap B=\{3\}$$
Is her solution correct? If not, identify all her mistakes.
Yes. The whole solution is perfectly fine.
No, her solution is not correct. The only mistake is in step (2).
The corrected set $B=\{-3,-2,-1,0,1,2\}$, and so the sought intersection is empty, $A\cap B=\emptyset$.
No, her solution is not correct. The only mistake is in step (1).
The corrected set $A=\{-3,3\}$, leading to the intersection $A\cap B=\{-3,3\}$.
No, her solution is not correct. The mistakes are in steps (1) and (2).
The corrected set $A=\{-3,3\}$, the corrected set $B=\{-3,-2,-1,0,1,2\}$, and so the sought intersection is $A\cap B=\{-3\}$.