I'm pretty sure similar question was asked, so sorry that I'm posting this again, but just reading the answers on that question didn't seem to provide enough insight for me and I'd just like to double-check if I'm getting this right and doing it correctly. Basically I have some info on natural deduction and one example:
Aim to show: $$\begin{align} &p\land q \vdash q \land p \\ &1. p \land q - premise \\ &2. p - \land e_1 \ 1\\ &3. q - \land e_2 \ 1\\ &4. q \land p - \land i \ \ 3,2 \\ \end{align}$$
So as I understand, I can assume that p and q are true and following the elimination rules first eliminate them (p in 2nd line by elimination 1st rule, q in 3rd line by elimination 2nd rule) and then again by the same assumption they're true I can introduce $ \land $ and make $ q \land p $ in the 4th line from 3rd and 2nd line. I don't know if I at least sort of get it or I'm way off, but I've tried to do another example (it has no solution example) and if someone wouldn't mind, I'd like to ask if I got it right, so here's another example:
Aim to show: $$\begin{align} &p \land (q \land r) \vdash (p \land q) \land r \\ &1. p \land (q \land r) - premise \\ &2. p - \land e_1 \ 1 \\ &3. q \land r - \land e_2 \ 1 \\ &4. q - \land e_1 \ 3 \\ &5. r - \land e_2 \ 3 \\ &6. p \land q - \land i \ 2,4 \\ &8. (p \land q) \land r - \land i \ 6,5 \\ \end{align}$$
Is this correct or not? Since proving by natural deduction seems a bit weird for me, compared to all other stuff that I've been doing and I don't know if I get it at least half right.