Show ${\neg \ p \ \cup \neg \neg \ q}\equiv{\neg p \ \cup q}$

Question

I'm currently working in the following excercise:

Show $${\neg \ p \ \cup \neg \neg \ q}\equiv{\neg p \ \cup q}$$

I've been thinking a way of applying the laws I've learned in class but I'm still unable to, I started applying DeMorgan's laws but still cannot find a good path to follow.

Any hint or help will be really appreciated, thank you for taking the time to read my question.

Answer 1

Well, you mean $\neg p\vee \neg\neg q \Longleftrightarrow \neg p\vee q$. Here one just needs to note that $\neg\neg q \Longleftrightarrow q$, the law about double negation. No need to use De Morgan.