A Logical Approach to Discrete Mathematics: https://www.amazon.com/Logical-Approach-Discrete-Monographs-...
And a more pragmatic approach to the same material (with a lot of cross-over in terms of proof-style, etc):
Programming in the 1990s: http://www.springer.com/gp/book/9780387973821
But one I particularly enjoyed early on was written for liberal-arts level students of maths (who might've been traumatized by maths in the past):
Introduction to Graph Theory: https://www.amazon.com/Introduction-Graph-Theory-Dover-Mathe...
It will actually get you into writing proofs in set theory within the first couple of chapters.
To add to the fire: