Simplifying this Boolean expression

Question

How do you simplify this expression?

$$\lnot[\lnot[(P \lor Q) \land R] \lor \lnot Q] \equiv Q \land R$$

I understand the laws used but still not getting the exact answer. I would appreciate if someone solved this for me.

Answer 1

\begin{eqnarray} \lnot[\lnot[(P\lor Q)\land R]\lor \lnot Q] &=& [(P\lor Q)\land R] \land Q \\ &=& [(P\land R)\lor (Q\land R)] \land Q \\ &=& (P\land R\land Q) \lor (Q\land R) \\ &=& (P\land A) \lor A ~~~\mbox{where}~~~ A = Q\land R\\ &=& A = Q \land R \end{eqnarray}