To convert the propositional formula $(P \lor (Q \land R)) \rightarrow (\neg P \land \neg Q)$ into conjunctive normal form (CNF), we follow a step-by-step approach.

Step 1: Rewriting the implication

The implication $A \rightarrow B$ can be rewritten as $\neg A \lor B$. So, we rewrite the formula as:

$\neg (P \lor (Q \land R)) \lor (\neg P \land \neg Q)$

Step 2: De Morgan's Law on the negation

Apply De Morgan's Law to the negation $\neg (P \lor (Q \land R))$:

$(\neg P \land \neg (Q \land R)) \lor (\neg P \land \neg Q)$

Step 3: Simplifying the second negation

Using De Morgan's Law again for $\neg (Q \land R)$, we get:

$(\neg P \land (\neg Q \lor \neg R)) \lor (\neg P \land \neg Q)$

Step 4: Distribute the conjunction over the disjunction

Now, distribute the conjunction $(\neg P \land (\neg Q \lor \neg R))$ over $\lor$, applying the distributive property:

$(\neg P \lor (\neg P \land \neg Q)) \land (\neg P \lor (\neg P \land \neg R)) \lor (\neg P \land \neg Q)$

Now the expression can be simplified. Let's take the simplest CNF form for the formula:

Final Answer:

The CNF equivalent of the propositional formula is:

[ (\neg P \lor \neg