I discover this in All NP problems reduce to NP-complete problems: so how can NP problems not be NP-complete?

- If problem B is in P and A reduces to B, then problem A is in P.
- Problem B is NP-complete if B is in NP and for every problem in A in NP, A reduces to B.
- Problem C is NP-complete if C is in NP and for some NP-complete problem B, B reduces to C.

My questions are (if **I** then **II** then(?) **III/I**. If **III/I** and **III/II** then **IV**.)

**I**: Are there a generalized form to reduces NP problem to either P or NP-complete?**II**: Are there a certain number of NP-complete problems?**III/I**: Are all of the NP-complete problems can be reduces to all other NP-problems?**III/II**: If we can reduce B in NP-complete problem to A in P, can we prove that all problem reduces to B is in P?**IV**: If we prove that there is an NP-complete problem that is P, Can we consider that P=NP?