# RE5 | openai/gpt-5.4-mini | run 1

## Prompt

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

## Response

No. The conclusion does **not** logically follow.

## Why
The statements are:

- All roses are flowers.
- Some flowers fade quickly.

From this, you only know that **at least one flower** fades quickly. You do **not** know that any of those quickly fading flowers are roses.

## Counterexample
Imagine a world where:

- All roses are flowers.
- The only flowers that fade quickly are tulips.
- No roses fade quickly.

Both premises are true, but the conclusion “some roses fade quickly” is false. So the argument is invalid.

## Formally
The premises support:

- \( \forall x (R(x) \rightarrow F(x)) \)
- \( \exists x (F(x) \land Q(x)) \)

But they do not imply:

- \( \exists x (R(x) \land Q(x)) \)

Would you like me to show this using a Venn diagram or symbolic logic?
