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2.4 DEDUCTIVE REASONING Playing the game of logic well Law of Detachment [(p>>q)^p]>>q If p, then q is True And p is True Then q is True An example: If a vehicle is a car, then it has four wheels. A Cadillac is a car. Then (by the law of detachment) it (the caddy) has four wheels. Law of Syllogism [(p>>q)^(q>>r)] >>(p>>r) If p, then q is True And If q, then r is True Then If p, then r is True An example: If Gertrude takes the Cadillac for a spin, she will stop at the post office. If she stops at the post office, then she will buy stamps. Thus (by the law of syllogism) If Gertrude takes the Cadillac for a spin, then she will buy stamps. Cornerstone of Geometry These are two of the laws of logic that provide a system for reaching logical and always true conclusions. This system is called Deductive Reasoning