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The question asks which expressions are equivalent to \( p \lor q \) (which reads as "p or q"). We can analyze each option using propositional logic equivalences.

Let's evaluate each expression:

1. **\( q \rightarrow \neg p \)**: 
   This means "if q, then not p." This is not logically equivalent to \( p \lor q \), because \( p \lor q \) is true when either \( p \) or \( q \) is true, whereas \( q \rightarrow \neg p \) doesn't capture that truth table.

2. **\( q \lor p \)**:
   This is exactly the same as \( p \lor q \) because disjunction (OR) is commutative. So, this is equivalent to \( p \lor q \).

3. **\( p \rightarrow q \)**:
   This means "if p, then q." This is not equivalent to \( p \lor q \). The truth tables differ significantly.

4. **\( \neg q \rightarrow p \)**:
   This is logically equivalent to \( p \lor q \) because of the implication equivalence \( \neg q \rightarrow p \equiv p \lor q \). So, this is an equivalent expression.

5. **\( \neg p \rightarrow q \)**:
   This is logically equivalent to \( p \lor q \) by the same reasoning as above (using the contrapositive form). So, this is also equivalent.

6. **\( q \land p \)**:
   This is "q and p," which is not equivalent to \( p \lor q \) because \( p \land q \) is true only if both \( p \) and \( q \) are true, unlike \( p \lor q \).

7. **\( \neg p \land \neg q \)**:
   This is the negation of \( p \lor q \) (using De Morgan’s law). It’s the exact opposite of \( p \lor q \), so this is not equivalent.

### Correct answers:
- \( q \lor p \)
- \( \neg q \rightarrow p \)
- \( \neg p \rightarrow q \)

Would you like further details or have any additional questions?

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**Related Questions:**
1. What is the truth table for \( p \lor q \)?
2. How do De Morgan's laws relate to conjunction and disjunction?
3. What are the key differences between implication and disjunction?
4. How does contraposition work in propositional logic?
5. Can you provide the truth table for \( \neg p \land \neg q \)?

**Tip:** Implication (\( \rightarrow \)) can often be rewritten as a disjunction using the equivalence \( p \rightarrow q \equiv \neg p \lor q \).

Which expressions are equivalent to p ∨ q? (Select all equivalent expressions.)

Identify equivalent expressions to p ∨ q in propositional logic by analyzing disjunctions, implications, and logical equivalences. The problem covers key logic principles such as De Morgan's laws and the contrapositive. Suitable for university students studying logic or discrete math.

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