https://file.aiquickdraw.com/mathbot/file/1726266716486orl11w25.jpg

The argument in the image can be written as:

1. \( p \lor q \)  (Premise)
2. \( \neg q \) (Premise)
3. \( \therefore p \) (Conclusion)

This is a standard argument form known as **disjunctive syllogism**. 

Disjunctive syllogism states that if we have \( p \lor q \) (meaning "either \( p \) or \( q \)") and \( \neg q \) (meaning "not \( q \)"), then \( p \) must be true.

Since this argument follows this valid form, the argument is **valid**.

Do you want more details or have any questions?

Here are 5 related questions to explore further:
1. What are other examples of valid argument forms?
2. How does modus ponens differ from disjunctive syllogism?
3. Can you explain the difference between a valid and sound argument?
4. What is a common logical fallacy that can make an argument invalid?
5. How do logical connectives like \( \lor \) and \( \neg \) function in propositional logic?

**Tip**: In propositional logic, learning common valid argument forms like modus ponens, modus tollens, and disjunctive syllogism can help you easily determine the validity of an argument.

Determine whether the following argument is valid, using the given forms of valid arguments and fallacies: p ∨ q, ~q, ∴ p

This example demonstrates the use of disjunctive syllogism in propositional logic to determine the validity of an argument. Given the premises p ∨ q and ~q, it logically follows that p must be true. Learn how this valid form of argument works in logic.

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