Are there any good Discrete mathematics learning web resources with problem sets?
I have the perfect place for you, I really enjoyed it myself:
Everything I learned is from that site.
There is a whole course being offered by Udacity*, Logic and Discrete Mathematics, which has interactive quizzes and homework assignments.
The course description is as follows:
This course presents key concepts in discrete mathematics, specifically, elementary propositional logic and elements of enumerative combinatorics, elementary number theory, and graph theory, with partially ordered sets and lattices as a unifying concept.
*I am not affiliated with them in any way, but I have taken some of their prior courses
Kenneth Rosen's text "Discrete mathematics and its applications" is available on archive.org's opensource collection here. The PDF of the ebook can be downloaded (legally, it looks like).
Rosen's text is a classic for introductory discrete mathematics. Solutions to odd-numbered exercises are in the book.