Where to study the basics of solving logical problems with elements of mathematical analysis, Boolean logic?

Question

Mathematics

Had fun at GeekBrains trying to solve the attached puzzles. I realized that I was completely swimming in the topic. I wanted to ask where you can get acquainted with such topics.
PS Attached file with examples

Answer 1

1. In books on mathematical logic.
   
2. Mathematical analysis has nothing to do with this.
   
3. What is "vile", I do not know.
   

Answer 2

I warmly recommend Raymond Smallian's The Princess or the Tiger.
There, in simple language, logic and combinatorics are perfectly explained using the example of stories and characters. The whole book is built from simple to very difficult problems.
If you master the whole book (not just read, but understand the solution of the final tasks) - I take off my hat. For about 25 years, from about the middle of the book, I have been reading it only as art literature =)