Can cats and dogs mate?

Cats and dogs cannot mate with each other, even if it looks like they're trying to do so. Their breeding behaviors, heat cycles, and different DNA prevent them from being able to produce healthy, viable offspring. Hybrid species can be created when the animals have similar DNA to each other, such as lions and tigers.

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And another question, do male lions mate with their sisters?

Yes, lions can mate with their siblings either knowingly or unknowingly. You will see the same dominating male lion mating with most of the lioness in the same group or with a different group. In respect to this, do tigers mate with their siblings? But male tiger cubs sometimes stick around after leaving their mothers & with time if they manage to replace their fathers as dominant male of the region, they have been known to get into sexual relationships? with their sisters, step-sisters (from a different litter) & sometimes even their mother.