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Let’s analyze the provided question and solve it step-by-step:

### Problem Summary:
1. **Let \( p \):** "15 is an odd number"  
   This is **true** because 15 is indeed an odd number.

2. **Let \( q \):** "21 is a prime number"  
   This is **false** because 21 is not a prime number (it can be factored as \( 3 \times 7 \)).

We now evaluate each logical statement based on \( p \) being **true** and \( q \) being **false**.

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### Logical Statements to Evaluate:
1. **\( p \lor q \) (p OR q):**
   - OR is true if at least one of \( p \) or \( q \) is true.
   - Here, \( p \) is true and \( q \) is false.
   - \( p \lor q = \text{true} \).

2. **\( p \land q \) (p AND q):**
   - AND is true only if both \( p \) and \( q \) are true.
   - Here, \( p \) is true but \( q \) is false.
   - \( p \land q = \text{false} \).

3. **\( p \implies q \) (p implies q):**
   - Implication \( p \implies q \) is false only if \( p \) is true and \( q \) is false.
   - Here, \( p \) is true and \( q \) is false.
   - \( p \implies q = \text{false} \).

4. **\( \neg q \implies p \) (NOT q implies p):**
   - First, evaluate \( \neg q \) (NOT q). Since \( q \) is false, \( \neg q \) is true.
   - Implication \( \neg q \implies p \) is true if \( \neg q \) is true or \( p \) is true.
   - Both \( \neg q \) and \( p \) are true.
   - \( \neg q \implies p = \text{true} \).

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### Correct Statement:
From the evaluation above:
- \( p \lor q = \text{true} \)
- \( p \land q = \text{false} \)
- \( p \implies q = \text{false} \)
- \( \neg q \implies p = \text{true} \)

Thus, **the correct statements are \( p \lor q \) and \( \neg q \implies p \)**.

Let me know if you’d like further clarification!

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### Related Questions:
1. What is the difference between conjunction (\( \land \)) and disjunction (\( \lor \)) in logic?
2. Can you explain why \( p \implies q \) is false in this case?
3. How is the truth value of an implication (\( \implies \)) determined in logic?
4. What are prime numbers, and why is 21 not prime?
5. How would the answers change if \( q \) were true instead?

### Tip:
In logic, **implications** \( p \implies q \) are tricky because they are true except when \( p \) is true and \( q \) is false. Always evaluate implications carefully!

Let p: 15 is an odd number. Let q: 21 is a prime number. Which of the following statement is correct about p ∨ q, p ∧ q, p ⇒ q, and ¬q ⇒ p?

Understand propositional logic by analyzing the statements p ∨ q, p ∧ q, p ⇒ q, and ¬q ⇒ p. This problem explores logical OR, AND, implications, and negations with a detailed step-by-step solution. Suitable for Grades 9-12 students.

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