I am getting ready for finals, and encountered this question in a past assignment. I haven't proved this then and I don't understand how I can prove it now.
Prove\Disprove: If $L_1$ is not a Context-Free language, and $L_2$ is finite, then $L_1 \cup L_2$ is not a Context-Free language.
My intuition says this is true, but we haven't really seen properties of none CFL's in the course, so i'm having a hard time coming up with a solution based solely on closure of operations on CFL's and RL's.
any helpful insight would be great, thank you!