The logical expression $(\neg p \lor q) \land (\neg q \lor p)$ is equivalent to p ≡ q, which means $p$ is logically equivalent to $q$. In other words, $p$ and $q$ always have the same truth value (both true or both false).

Step-by-Step Simplification:

1. Express the original statement:
   $(\neg p \lor q) \land (\neg q \lor p)$.

2. Rewrite each term using implications equivalence:

   • $\neg p \lor q$ is equivalent to $p \implies q$.
   • $\neg q \lor p$ is equivalent to $q \implies p$.

   Therefore, the entire expression becomes:
   $(p \implies q) \land (q \implies p)$.

3. Combine implications:
   The conjunction $(p \implies q) \land (q \implies p)$ means $p$ and $q$ imply each other. This is the definition of logical equivalence: $p \equiv q$.

4. Final Answer:
   $(\neg p \lor q) \land (\neg q \lor p) \equiv p \equiv q$.

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Would you like more details or have any further questions?
Here are related questions for practice:

1. Simplify $(p \lor q) \land (\neg p \lor q)$.
2. What is the truth table for $p \equiv q$?
3. Prove $(p \implies q) \land (q \implies p) \equiv p \equiv q$ using a truth table.
4. How is $p \equiv q$ different from $p \oplus q$ (exclusive OR)?
5. What is the dual of $(\neg p \lor q) \land (\neg q \lor p)$?

Tip: Logical equivalence can be visualized with truth tables to verify all truth values match perfectly.