https://file.aiquickdraw.com/mathbot/file/172686694952949pz00zu.jpg

Let's break this down step by step to solve the problem.

The argument given in the image is as follows:

- **Premise 1:** If he likes to eat steak, he will not go out to eat.
- **Premise 2:** He will go out to eat.
- **Conclusion:** He does not like to eat steak.

### Step 1: Translating the Statements into Symbolic Form
Let:
- \( p \) = "He likes to eat steak."
- \( q \) = "He will go out to eat."

In symbolic logic:
- **Premise 1** translates to: \( p \rightarrow \neg q \) (If he likes to eat steak, then he will not go out to eat).
- **Premise 2** translates to: \( q \) (He will go out to eat).
- **Conclusion** translates to: \( \neg p \) (He does not like to eat steak).

### Step 2: Validity of the Argument
The structure of the argument is:

1. \( p \rightarrow \neg q \)
2. \( q \)
3. Therefore, \( \neg p \)

This is an application of **Modus Tollens**, which is a valid argument form. In Modus Tollens, the form is:

1. \( p \rightarrow \neg q \)
2. \( q \)
3. Therefore, \( \neg p \)

Since the conclusion logically follows from the premises, **the argument is valid**.

### Step 3: Answer
The correct answer is:
- **Option A:** The argument is valid. In symbolic form, the argument is \( p \rightarrow \neg q, q, \therefore \neg p \).

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Would you like a detailed explanation of how Modus Tollens works or any other clarifications?

Here are 5 questions to consider:
1. How can you construct truth tables to verify the validity of logical arguments?
2. What is the difference between Modus Ponens and Modus Tollens?
3. How do logical fallacies relate to invalid argument forms?
4. What other valid argument forms exist in propositional logic?
5. How would the conclusion change if one of the premises were false?

**Tip:** Remember that Modus Tollens is one of the most common logical forms used in everyday reasoning. It allows you to deny the antecedent when the consequent is proven false.

Translate each argument into symbolic form. Then determine whether the argument is valid or invalid.

Learn how to translate logical arguments into symbolic form and assess validity using the Modus Tollens theorem. This step-by-step guide explains how to analyze arguments and determine whether they are valid or invalid, suitable for college-level logic students.

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