I need help with the following mock exam questions. True or false?
1.) If a non-trivial $(\neq \emptyset, \Sigma^*)$ finite set is NP-complete, then $P = NP$.
True. Every finite set is in $P$ and because of the $NP$-completeness every set in $NP$ can be reduced to this set. Is it right?
2.) $NP \subseteq coNP$ $\Leftrightarrow$ $NP = coNP$.
I don't know if the "$\Rightarrow$" case holds. I only know $P \subseteq coNP$ and $P \subseteq NP$.
3.) For every fixed $k$ the problem $k$-$CLIQUE$ can be modeled as a Constraint Satisfaction Problem.
I have no idea. We've had $3$-$COLOR$ and $3$-$SAT$ as examples but also the fact that not every NP-problem can be expressed in terms of a CSP.
Thanks in advance!