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Let's analyze the truth table to check if it is correct for the given logical statement \( p \rightarrow \neg q \) (read as "if \( p \), then not \( q \)").

Here’s how we approach the problem:

1. **Given Statement**: \( p \rightarrow \neg q \)
2. **Negation of \( q \)** (\( \neg q \)): 
   - \( q = T \), then \( \neg q = F \)
   - \( q = F \), then \( \neg q = T \)

3. **Implication** \( p \rightarrow \neg q \):
   - Implication \( p \rightarrow \neg q \) is false only if \( p = T \) and \( \neg q = F \) (i.e., \( p = T \) and \( q = T \)). Otherwise, it is true.

Now, let's check the table:

| \( p \) | \( q \) | \( \neg q \) | \( p \rightarrow \neg q \) |
|--------|--------|-------------|--------------------------|
| T      | T      | F           | F                        |
| T      | F      | T           | T                        |
| F      | T      | F           | T                        |
| F      | F      | T           | T                        |

### Comparison with the provided table:
The table you uploaded shows:

| \( p \) | \( q \) | \( p \rightarrow \neg q \) |
|--------|--------|--------------------------|
| T      | T      | F                        |
| T      | F      | T                        |
| F      | T      | T                        |
| F      | F      | T                        |

It matches the correct truth table for \( p \rightarrow \neg q \), so **yes, the truth table is correct**.

Would you like more details on truth tables or implications? Here are some related questions:

1. How does the implication \( p \rightarrow q \) work logically?
2. What happens if both \( p \) and \( q \) are false in an implication?
3. Can you explain the difference between \( p \rightarrow q \) and \( q \rightarrow p \)?
4. What is the significance of the negation \( \neg q \) in logical statements?
5. How would a truth table look for the expression \( \neg (p \wedge q) \)?

**Tip**: In logic, an implication is only false when the first part is true, and the second part is false.

Verify the truth table for the logical expression p -> ~q, which involves key concepts in propositional logic such as implication and negation. This is suitable for high school students learning about logic in Grades 10-12.

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