I am facing the following question:
Let $\Pi$ and $\Pi$’ be two NP-complete problems, prove or refute $\Pi’\propto_{poly}\Pi$.
I do not understand the meaning of this question and how to answer it.
The definition of $\Pi’\propto_{poly}\Pi$" as follows:
Let $\Pi$ and $\Pi'$ be two decision problems. We say that $\Pi$ reduces to $\Pi'$ in polynomial time, symbolized as $\Pi’\propto_{poly}\Pi$, if there exists a deterministic algorithm $A$ that behaves as follows. When $A$ is presented with an instance $I$ of problem $\Pi$, it transforms it into an instance $I’$ of problem $\Pi'$ such that the answer to $I$ is yes iff the answer to $I’$ is yes. Moreover, this transformation must be achieved in polynomial time.