Re: 2 true/false NP complexity related questions

In article <1173999737.390019.95770@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
cooldavid <vmvictorvm@xxxxxxxxx> wrote:
1. No problems in NP can be solved in polynomial time.
ANS: Unknown (We don't know)

For #1, I think the answer should be FALSE. Because P is a subset of
NP. Am I right? So a problem in P is also in NP. Therefore some
problems in NP can be solved in polynomial time(Those that are in P).

That's right.

2. X is in NP and X <=p SAT. Then X is NP-complete
ANS: False

For #2, by we learned that for X to be NP-complete, it must be in NP
AND as hard as all the NP-complete problem. So Isn't #2 should be
True?

#2 would be true if you replaced "X <=p SAT" by "SAT <=p X" for the reasons
that you state, but as it stands it is false because the reduction goes in
the wrong direction.
--
Tim Chow tchow-at-alum-dot-mit-dot-edu
The range of our projectiles---even ... the artillery---however great, will
never exceed four of those miles of which as many thousand separate us from
the center of the earth. ---Galileo, Dialogues Concerning Two New Sciences
.