Simplifying a logical statement - need further advice

Question

I am having issues simplying the following statement any further: $$\lnot p \land \lnot q \land (p \lor q \lor \lnot r)$$

According to the solution, the answer is $$\lnot p \land \lnot q \land \lnot r$$

Can't quite figure it out. Any hints would be much helpful.

Answer 1

Note that $\bar{a} a $ is always false.

$\bar{p} \bar{q} (p +q+\bar{r}) = \bar{p}(\bar{q}p +\bar{q}q+\bar{q}\bar{r})= \bar{p}(\bar{q}p +\bar{q}\bar{r}) = \bar{q}\bar{p}p +\bar{p}\bar{q}\bar{r} = \bar{p}\bar{q}\bar{r}$