Looking for a Great book on Proving, on Mathematical Logic in general I'm looking for a good/great book on Mathematics. More specifically one that focuses on how I should go about to prove various things, e.g. given equations what are the methods I can use in order to solve them. Generally, I mostly want a book about logic, a book that organizes one's ability to reason and not fall into traps of logical fallacies. I have found this book by David Hilbert to be more or less what I want (I think). What are your thoughts and suggestions? Thanks in advance.

Kenneth Rosen's Discrete Math and its Applications 
A Concise Introduction to Logic by Patrick J. Hurley 
The former is an intro to proof text and the latter is not a math text but it has considerable examples of logical fallacies. 
