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Such categories are only an approximation of reality to help with classification. There is stuff like ring species [1] for example or species complex [2].

[1]: https://en.wikipedia.org/wiki/Ring_species

[2]: https://en.wikipedia.org/wiki/Species_complex

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Any known ring species where (A + B cannot breed OR B + C cannot breed) AND A + B can breed? Assume not possible?

You are asking for both A&B and !(A&B)?

That's logically equivalent to (A + B can breed) AND (B + C cannot breed), not a very exciting question.

Did you mean AND (A + C can breed)?

Still not exciting. I think we are looking for non transitivity: A+B & B+C but !A+C

That's exactly what a ring species is.

Thanks for fixing. Yes that was the intended question.

Very helpful links, I didn't know the term ring species

I thought that unlike what was previously thought, there are no known examples of ring species.

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