Okay, so suppose we agree to limit ourselves to deductive reasoning. In an attempt to answer these questions, Aristotle developed a catalog of correct reasoning patterns, called syllogisms. The first pattern shown above is one of these. There are several more, but Aristotle suspected that his list was not complete. One of the interesting results of modern logic is the realization that only a small number of such patterns are necessary to derive all correct conclusions from a given set of premises.
Additional patterns are possible, but they add nothing in deductive power.
Computational Mathematics 1. Formal Language for encoding information. Legal transformations 3. Xavier's age and Yolanda's age add up to twelve. If Mary loves Pat, then Mary loves Quincy.