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Reasoning and Proof Deductive Reasoning
Deductive reasoning • Deductive reasoning is one of the two basic forms of valid reasoning. It begins with a general hypothesis or known fact and creates a specific conclusion from that generalization. This is the opposite of inductive reasoning, which involves creating broad generalizations from specific observations. The basic idea of deductive reasoning is that if something is true of a class of things in general, this truth applies to all members of that class. One of the keys for sound deductive reasoning, then, is to be able to properly identify members of the class, because incorrect categorizations will result in unsound conclusions. • A generalization might be something such as, "All wasps have stingers. " The logical conclusion of a specific instance would then be, "That is a wasp, so it has a stinger. " This is a valid deduction.
Two important laws • Law of Detachment – Law of Detachment says that if p → q is true and p is true, then q must be true. – ((p→q)Λp)→q • Law of Syllogism – takes two conditional statements and forms a conclusion by combining the hypothesis of one statement with the conclusion of another. If p →q and q →r are true then p →r is also true – ((p →q)Λ(q →r)) →(p →r)