# Is $\Pi’\propto_{poly}\Pi$ for any two NP-complete problems $\Pi,\Pi'$?

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.

1. A problem $$\Pi$$ is NP-hard if $$\Pi' \propto_{\mathit{poly}} \Pi$$ for every $$\Pi'$$ in NP.
2. A problem $$\Pi$$ is NP-complete if $$\Pi$$ is NP-hard and $$\Pi$$ is in NP.