> ¬A (not profitable) => B (startup)
> does not imply
> A (profitable) => ¬B (not a startup)
does not imply that ¬A => B. In other words, the logical structure can be correct, but that does not mean the premises are themselves true. This is the difference between validity and soundness in formal logic [0].
[0] https://iep.utm.edu/val-snd/
> ¬A (not profitable) => B (startup)
> does not imply
> A (profitable) => ¬B (not a startup)
does not imply that ¬A => B. In other words, the logical structure can be correct, but that does not mean the premises are themselves true. This is the difference between validity and soundness in formal logic [0].
[0] https://iep.utm.edu/val-snd/