# On intersection of classes [closed]

Consider classes $\mathcal C_1$ and $\mathcal C_2$ of problems both of which are $\mathsf{NP}$-complete. Does it mean $\mathcal C_1\cap\mathcal C_2$ of problems is $\mathsf{NP}$-complete?

## closed as unclear what you're asking by D.W.♦Apr 29 '16 at 3:11

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

• It's not clear what you mean by "class of problems...[is] NP-complete", so the problem doesn't seem well-specified at present. The definition of NP-completeness applies to problems, not classes of problems. Please edit the question to clarify what you are asking. Also, as always, you should show your thoughts and what thinking you've already done. – D.W. Apr 29 '16 at 3:10
• The title you have chosen is not well suited to representing your question. Please take some time to improve it; we have collected some advice here. Thank you! – D.W. Apr 29 '16 at 3:11

In any case, it sounds like it's possible that $\mathcal{C}_1\cap\mathcal{C}_2 = \emptyset$, in which case the answer seems to be "no". (Well, except that every problem in $\emptyset$ is NP-complete, in which case the answer would be "yes" but for vacuous reasons.)