Question about proving de morgan's law by natural deduction

Question

This is my practice on this question, but I don't know if my answer is right or not. If it's wrong, please tell me which part goes wrong and how to do it. Thanks!

Answer 1

That's essentially correct. I don't know if you're using a specialized flavor of $\vee E$, but here's my derivation in http://proofs.openlogicproject.org/.

Answer 2

No, your proof has a number of mistakes.

First, from line 14, I gather PC is Proof by Contradiction ... which makes its applications on lines 8 and 11 incorrect: from the subproof on lines 6-7, you can only conclude $\neg \neg a$, and from 9-10 you conclude $\neg \neg b$, not what you have.

Also, your use of $\lor E$ on line 12 is incorrect.

Ok, so how do you do it? For that, see Matt Daly's answer.