# RE5 | google/gemini-3.6-flash | run 1

## Prompt

All roses are flowers. Some flowers fade quickly. Does it logically follow that some roses fade quickly? Explain.

## Response

No, it does not logically follow that some roses fade quickly. While all roses are classified as flowers and certain flowers fade quickly, those quickly fading flowers could consist entirely of species other than roses. For a logical deduction to be valid, the conclusion must be guaranteed to be true whenever the premises are true.

## Logical Breakdown

Categorical logic demonstrates why the argument is invalid by examining set relationships:

* **Premise 1:** All roses are flowers (\( R \subseteq F \)). The set of roses is entirely contained within the set of flowers.
* **Premise 2:** Some flowers fade quickly (\( F \cap Q \neq \emptyset \)). An intersection exists between the set of flowers and the set of items that fade quickly.
* **Conclusion:** Some roses fade quickly (\( R \cap Q \neq \emptyset \)). This asserts an intersection between roses and items that fade quickly.

Because Premise 2 only establishes that *some* flowers fade quickly, it does not specify *which* flowers do so. The subset of flowers that fade quickly does not necessarily overlap with the subset of flowers that are roses.

## Counterexample

To illustrate the flaw in reasoning, consider a scenario where the set of flowers consists of two groups: roses and tulips.

* All 50 roses are flowers.
* 10 tulips fade quickly, making the statement "some flowers fade quickly" true.
* 0 roses fade quickly.

In this scenario, both premises are strictly true, yet the conclusion is false. Because a valid deductive argument requires the conclusion to hold in 100% of scenarios where the premises are true, the argument is deductively invalid.

## Fallacy Classification

This formal argument commits the **fallacy of the undistributed middle**. The middle term ("flowers") connects the subject ("roses") and the predicate ("things that fade quickly"). However, because the middle term is not distributed in either premise—meaning neither premise refers to *all* flowers fading quickly—it fails to establish a mandatory logical link between roses and quick fading.

Would you like to analyze another logical syllogism or learn how to test categorical arguments using Venn diagrams?
