https://file.aiquickdraw.com/mathbot/file/172573347242982jy0j37.jpg

The argument in the image asks you to determine the validity of the following statement:

\[
p \rightarrow q, \sim q \vdash \sim p
\]

This can be interpreted as determining if the argument is valid, where:

1. \( p \rightarrow q \) (If \( p \), then \( q \)).
2. \( \sim q \) (Not \( q \)).
3. Conclusion: \( \sim p \) (Not \( p \)).

### Logical Structure:
We need to verify whether the premises logically imply the conclusion. This is an instance of **Modus Tollens**, a valid form of deductive reasoning.

- **Modus Tollens**: If \( p \rightarrow q \) and \( \sim q \) are both true, then \( \sim p \) must be true.

In this case:
1. Premise 1: \( p \rightarrow q \) states that if \( p \) is true, then \( q \) must be true.
2. Premise 2: \( \sim q \) states that \( q \) is false.
3. From this, we can conclude that \( p \) must be false (i.e., \( \sim p \)).

### Conclusion:
This argument is **valid** because it follows the Modus Tollens rule of inference. Therefore, the premises logically imply the conclusion.

Let me know if you'd like further clarification or have any questions! Here are some related questions to explore:

1. What is the difference between Modus Ponens and Modus Tollens?
2. How can we prove the validity of an argument using truth tables?
3. What are some common fallacies that might arise in logical reasoning?
4. How does contraposition relate to Modus Tollens?
5. How can we use formal proofs to validate logical arguments?

**Tip:** In logic, always try to identify the form of the argument (like Modus Ponens or Modus Tollens) to quickly assess its validity.

Determine the validity of the argument: p → q, ∼q ⊢ ∼p.

Learn how to determine the validity of the logical argument: p → q, ∼q ⊢ ∼p. This problem covers key concepts in propositional logic and logical inference, specifically focusing on the Modus Tollens theorem. Suitable for students in Grades 10-12.

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