Suppose the following situation.
- You have a decision problem $D$.
- You know that $SAT$ is $NP$-complete.
- You know that $D\leq_p SAT$.
Can you conclude that $D\in NP$?
I think it's true because it means that $D$ is at least as hard as any other problem in $NP$.
As I know I am not able to post questions to answer with yes/no: If it's true, can you give a better explanation? If it's false, can you argue why is so?
PD: it's not homework.