# Types of Proofs

End With a Conclusion or QED Traditionally, the phrase is placed in its abbreviated form at the end of a mathematical proof or philosophical argument when the original proposition has been restated exactly, as the conclusion of the demonstration or completion of the proof.

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source: quizlet.com Rules of Inference and Logic Proofs A proof is an argument from hypotheses (assumptions) to a conclusion. Each step of the argument follows the laws of logic. In mathematics, a statement is not accepted as valid or correct unless it is accompanied by a proof. This insistence on proof is one of the things that sets mathematics apart from other subjects.

Work Through the Proof Backwards We work backwards to know where we're going, but we write forwards to make sure everything actually works. However, it is not always the case that proofs proceed from assumptions to goals. Here are two typical exceptions to the rule of start at the beginning and end at the end: Theorem: XXX. proof.

Write Down all Givens Write the steps down carefully, without skipping even the simplest one. Some of the first steps are often the given statements (but not always), and the last step is the conclusion that you set out to prove.

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