https://file.aiquickdraw.com/mathbot/file/1726868876338ixwymv3u.jpg

Let's break down the problem in the image step-by-step.

### Argument Translation:
You are given the following statements:

1. "We criminalize drugs or we damage the future of young people."
2. "We will not damage the future of young people."
3. "We criminalize drugs."

Let the statement **p** represent:
- \( p \): "We criminalize drugs."

Let the statement **q** represent:
- \( q \): "We damage the future of young people."

### Translating into Symbolic Form:
The argument can be translated as follows:

1. "We criminalize drugs or we damage the future of young people."
   - This becomes: \( p \lor q \) (read as "p or q").
   
2. "We will not damage the future of young people."
   - This becomes: \( \neg q \) (read as "not q").

3. Therefore: "We criminalize drugs."
   - This becomes: \( p \).

### Argument Structure:
The structure of the argument is:

\[
(p \lor q), \neg q \therefore p
\]

This is a **disjunctive syllogism**. In a disjunctive syllogism, if we have \( p \lor q \) and we know that \( q \) is false (i.e., \( \neg q \)), we can conclude that \( p \) must be true.

### Conclusion:
- The argument is **valid** because it follows the form of a valid disjunctive syllogism.

### Symbolic Form:
In symbolic form, the argument is:

\[
(p \lor q), \neg q \therefore p
\]

So, the correct answer is **A: The argument is valid.** In symbolic form, the argument is \( (p \lor q), \neg q \therefore p \).

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Do you need further clarification or any additional details? Here are some questions to explore this topic further:

1. What is a disjunctive syllogism, and why is it valid?
2. Can you provide an example of an invalid argument using a similar structure?
3. How can a truth table verify this argument’s validity?
4. What are the common forms of valid arguments in propositional logic?
5. Can we determine the validity of arguments with more than two propositions?

**Tip:** When translating arguments into symbolic form, always ensure that you clearly define each proposition to avoid confusion.

Translate the argument into symbolic form and determine whether it is valid or invalid. The given statements are: 'We criminalize drugs or we damage the future of young people', 'We will not damage the future of young people', and 'We criminalize drugs.'

Learn how to translate arguments into symbolic form using propositional logic. This example explores the disjunctive syllogism structure with the argument: 'We criminalize drugs or we damage the future of young people'. Determine its validity.

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