This is stuff that's usually taught in a course called "Discrete Mathematics". As far as textbooks go for this type of material, which do you all like? I own Rosen's famous book ( https://www.amazon.com/Discrete-Mathematics-Applications-Ken... ), but it's the "James Stewart's Calculus" of Discrete Mathematics books. I purchased some really old books too, but I haven't yet found one that I like a lot (I settled for a Dover text that's mostly passable).

For the specific topic of set theory, though, I haven't found one I like better than Paul Halmos: https://www.amazon.com/Naive-Theory-Undergraduate-Texts-Math...

If I could only find a number theory text that I like as much.