# RE5 | deepseek/deepseek-v4-pro | 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. The premises only tell us that roses are a subset of flowers, and that at least one flower fades quickly. They do not establish any overlap between roses and the quickly-fading things. The quickly-fading flowers could all be outside the rose subset.

### Logical structure

The argument has this form:

1. All R are F.  
2. Some F are Q.  
3. Therefore, Some R are Q.  

In categorical logic, this syllogism is invalid because the middle term F is distributed in neither premise (it is the predicate of a universal affirmative in premise 1 and the subject of a particular affirmative in premise 2). No valid conclusion about the relationship between R and Q can be drawn.

### Counterexample

A concrete case shows why the inference fails:

- Let **R** = {roses}  
- Let **F** = {roses, tulips}  
- Let **Q** = {tulips}  

Premise 1 holds: all roses are flowers.  
Premise 2 holds: some flowers (tulips) fade quickly.  
Conclusion fails: no rose is a tulip, so no rose fades quickly.

The premises would be just as true if roses never fade quickly — as long as some other kind of flower does. So the conclusion is not guaranteed.

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If the argument were reversed — *All roses are flowers, and some roses fade quickly* — we could validly conclude that *some flowers fade quickly*. But the original direction is a logical fallacy (the fallacy of the undistributed middle).
