"If A is nonregular, then there exists a nonregular language B such that A ∩ B is finite."?

Is the statement true?

I feel that the statement is true. I want to prove it but I don't know how to start the proof.

Any help would be appreciated.

• Remember, zero is a finite number. As Vladislav said in his answer, can you finish it now? Feb 27 '20 at 17:20

Clearly if $$A$$ is non-regular, its complement is non-regular as well. Can you finish it now?