When do you use that vs собака (sobaka)?
I don't, I'm Polish. Can't say for sure for Ukrainians, don't know Ukrainian that well, but my reading of https://en.wiktionary.org/wiki/%D1%81%D0%BE%D0%B1%D0%B0%D0%B... and https://en.wiktionary.org/wiki/%D0%BF%D0%B5%D1%81#Ukrainian suggests that пес must be male, but собака is either male or female. I might be wrong.
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I don't, I'm Polish. Can't say for sure for Ukrainians, don't know Ukrainian that well, but my reading of https://en.wiktionary.org/wiki/%D1%81%D0%BE%D0%B1%D0%B0%D0%B... and https://en.wiktionary.org/wiki/%D0%BF%D0%B5%D1%81#Ukrainian suggests that пес must be male, but собака is either male or female. I might be wrong.