Simplify the Proposition $$\Bigl(\bigl(P\lor Q\bigr)\land \lnot\bigr(\lnot P\land(\lnot Q\lor\lnot R)\bigl)\Bigr)\lor(\lnot P\land\lnot Q)\lor(\lnot P\land\lnot R)$$
What I've tried is simplify the $$\Bigl(\bigl(P\lor Q\bigr)\land \lnot\bigr(\lnot P\land(\lnot Q\lor\lnot R)\bigl)\Bigr)
$$ First , using the Distributive law i get
$$(P\lor Q) \land\lnot\bigl((\lnot P\land\lnot Q)\lor(\lnot P\land\lnot R)\bigr)$$
Using the DeMorgan Law and Double negation law i get
$$(P\lor Q)\land(P\land Q )\land(P \lor R)$$
Using the Idempotent law i get
$$(P\lor Q)\land (P\lor R)$$
and now i'm stuck
Best Answer
For your last line,
Use Distributive law (backward) you get
$$P\vee(Q\wedge R)$$