Question

Indicate whether each of the following statements are correct. JUSTIFICATION NEEDED.

(A) Suppose both problems $\Pi_{1}$ and $\Pi_{2}$ are in NP. If problem $\Pi_{1}$ is polynomial time reducible to $\Pi_{2}$ , and $\Pi_{1}$ is NP-complete, then so is $\Pi_{2}$ .

(B) Suppose both problems $\Pi_{1}$ and $\Pi_{2}$ are in NP. If problem $\Pi_{1}$ is polynomial time reducible to $\Pi_{2}$ , and $\Pi_{2}$ is NP-complete, then so is $\Pi_{1}$ .