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The problem asks us to use a truth table to determine whether the two logical statements are equivalent. The two statements are:

1. \( \sim p \rightarrow \sim q \)
2. \( \sim q \rightarrow p \)

Where:
- \( \sim p \) means "not p"
- \( \sim q \) means "not q"
- \( \rightarrow \) denotes implication (if... then...)

Let's construct the truth table for both statements.

We will analyze all possible truth values for \( p \) and \( q \) (True or False):

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

### Interpretation:
- In the third and fourth rows, the two statements yield different results. Therefore, the statements are **not equivalent**.

So, the correct answer is:

**The statements are not equivalent.**

Would you like any further details or clarifications?

Here are five follow-up questions for deeper understanding:
1. How do you interpret an implication in a truth table?
2. Why do the statements differ in truth values for specific combinations of \( p \) and \( q \)?
3. Can you find an example where similar statements would be logically equivalent?
4. How would changing the order of variables in an implication affect its truth value?
5. What is the relationship between contraposition and logical equivalence?

**Tip:** When checking logical equivalence, constructing a truth table is the most reliable method to compare two statements across all possible truth values.

Use a truth table to determine whether the two statements are equivalent: ∼p→∼q and ∼q→p.

This lesson walks through how to use a truth table to check the logical equivalence of two statements: ∼p→∼q and ∼q→p. Includes detailed truth table construction and analysis, focusing on implication and negation operations. Suitable for high school students learning propositional logic.

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