I'm a retired lecturer and recently put a whole lot of my notes on Set Theory and Logic on Wikibooks at
- Discrete mathematics/Set theory - Wikibooks, collection of open-content textbooks
- and Discrete mathematics/Logic - Wikibooks, collection of open-content textbooks
which might help you get started on these two topics. It's fairly basic stuff, with lots of worked examples, exercises and answers. And it's free! So help yourself, if you think it's any use.