Is the following assertion true or false?
If the language $L$ is NP-complete and $Q ⊆ L$, then $Q$ is NP-complete.
I know for example that $k$-coloring is NP-complete if I take $k$ as input, but 2-coloring is an infinite subset of this which is in P (see link). Therefore, for me, the assertion is false. However, I'm working through languages, and I cannot figure out an example (with language) useful to show false the assertion.