You need to learn that proving both A and B are true, is the same as proving neither one can be false. The classic example is "All men are mortal, Socrates is a man, hence Socrates is mortal", which is actually a bit more complicated since it also involves the "quantifier" word "all". The most famous principle is "modus ponens", namely if A is true and A implies B then B is also true. (The following book may be essentially the same, but I am not positive: The book I mentioned is hard to find at a good price, but any book that explains the propositional calculus, namely what does it mean to say a given statement is true, will do. If you don't know this, you are lost when some book tries to prove that every continuous function on is bounded, and they do so by starting out assuming the function is not bounded and concluding it is not continuous. when do you know a statement is true? A fundamental fact is the "contrapositive" principle, namely that to prove that A implies B, it is entirely equivalent to prove that B being false implies A is false also. Namely what does it mean to prove something? I.e. My experience in learning to do proofs was transformed when I read the first chapter of Principles of Mathematics, by Allendoerfer and Oakley, simply because it laid out the basic facts of the "propositional calculus".
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