I'm pretty new to logic and am having some struggles moving forward with this simplification. It's probably something small and silly that I'm missing but I've looked and can't figure out what it is. The original question asked is to simplify:
$$(p∧q)∧\neg(\neg p∧q)∧(q∧r)$$
And the solution is given to be:
$$(p\land q\land r)$$
After a few lines of working, I've come to this:
$$(p\land q\land r) \land (p \vee \neg q)$$
I used a logic table to ensure I'm still on the right track, so I do know that the original expression is logically equivalent to what I have above - but I am unsure of how to proceed in effectively removing the second parenthesised 'term'. I considered using the absorption law which looks almost the same but there's the extra $q$ and $r$ in there. I also tried to invert the distributive law but I noticed halfway through that I couldn't because of the order of $\land$'s and $\vee$'s. Any help is appreciated!
Use the distributive law to get $$(p \land q \land r \land p) \lor (p \land q \land r \land \lnot q)$$ and note that the right term vanishes (as it is impossible to fulfill) and the left term reduces to $$p \land q \land r$$