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The statement given in the image is:

**Construct a truth table for \( \sim q \rightarrow \sim p \). Use T for true and F for false.**

Here:
- \( \sim q \) represents the negation of \( q \),
- \( \sim p \) represents the negation of \( p \),
- \( \rightarrow \) is the implication operator ("if... then...").

Let's break it down and construct the truth table step-by-step.

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

### Explanation:
1. \( p \) and \( q \) take all combinations of True (T) and False (F).
2. \( \sim p \) is the negation of \( p \), and \( \sim q \) is the negation of \( q \).
3. The implication \( \sim q \rightarrow \sim p \) evaluates to False only when \( \sim q \) is True and \( \sim p \) is False, and True in all other cases.

Would you like more detailed reasoning or explanations on any particular step?

### Follow-up Questions:
1. What does the implication \( \rightarrow \) represent in logic?
2. How does negation affect the truth values of propositions?
3. Can you apply this truth table to a real-world scenario involving conditions \( p \) and \( q \)?
4. How would the truth table change if the operator were \( \leftrightarrow \) (biconditional)?
5. Can you extend this truth table to include three variables (e.g., \( p, q, r \))?

### Tip:
When constructing truth tables, always start by listing all possible combinations of truth values for the variables involved.

Construct a truth table for ∼ q → ∼ p. Use T for true and F for false.

Learn how to construct a truth table for ∼ q → ∼ p. This problem involves understanding propositional logic, negation, and implication. The solution includes step-by-step construction of the truth table with detailed explanations. Suitable for high school students in Grades 9-12.

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