The question asks to determine whether the two logical statements $P$ and $Q$ are equivalent. Let us carefully analyze the problem.

Statements:

1. $P: (\neg (p \land q)) \implies p$
2. $Q: (\neg p \lor \neg q) \implies p$

Step-by-Step Solution:

Step 1: Rewrite $P$

The statement $P: (\neg (p \land q)) \implies p$:

• $\neg (p \land q)$ can be rewritten using De Morgan's law as $\neg p \lor \neg q$.
• Thus, $P$ simplifies to: $(\neg p \lor \neg q) \implies p$

Step 2: Compare $P$ and $Q$

The rewritten form of $P$ is identical to the given $Q$: $Q: (\neg p \lor \neg q) \implies p$ Since both $P$ and $Q$ are the same expression, they are logically equivalent.

Final Answer:

P and Q are equivalent.

Do you want further clarification or details on this explanation?

Here are 5 related questions to explore further:

1. What are De Morgan's laws, and how are they used in simplifying logical statements?
2. How do you prove logical equivalence step by step using truth tables?
3. What does the logical implication operator ($\implies$) mean, and how can it be rewritten?
4. Can you give examples of logical statements that are not equivalent and explain why?
5. How does simplification of compound logical expressions help in problem-solving?

Tip: Always try rewriting logical statements in simpler forms (using laws like De Morgan's) before making comparisons!