(4 points) When we prove a problem X is NP-complete, it means X can solve all other problems

in NP (according to part 2 of the above definition). I.e., it means a fast solver for X could be used

to solve any problem in NP in poly-time. Does being NP-complete also mean X can be solved

by any other NP-complete problem? I.e., does it mean a fast solver for any other NP-complete

problem could in turn be used to solve X? Explain.

Hint: your answer to part (b) should reference the two parts of the definition of NP-completeness

1. X is in NP.

2. Any problem in NP is poly-time reducible to X. (I.e., for all Y NP, Y P X.)