## How to read and do proofs: an introduction to mathematical thought processThis straightforward guide describes the main methods used to prove mathematical theorems. Shows how and when to use each technique such as the contrapositive, induction and proof by contradiction. Each method is illustrated by step-by-step examples. The Second Edition features new chapters on nested quantifiers and proof by cases, and the number of exercises has been doubled with answers to odd-numbered exercises provided. This text will be useful as a supplement in mathematics and logic courses. Prerequisite is high-school algebra. |

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### Contents

J The Truth of It All | 1 |

TABLES Table 1 The Truth of P Implies E | 5 |

On Definitions and Mathematical Terminology | 23 |

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abstraction process angle answer an abstraction answer the abstraction assume backward process chapter choose method completing the proof condensed proof condensed version construction method contain an outline contains the quantifier contradiction method contrapositive method convex function convex set cos(t defining property desired conclusion desired object element equation equivalent Exercises Note forward process forward-backward method gives function f happens hence hypothesis of Example induction mathematics method gives rise numbers x obtain odd integer Outline of proof positive integer problem proof by contradiction proof machine Proof of Example proof technique proofs should contain proposition Prove Pythagorean theorem quadratic formula rational number reach a contradiction reach the conclusion right triangle XYZ satisfies the defining set namely shown sin(t specialization specific statement A implies statement containing statement is true Step subset symbol triangle is isosceles triangle RST Truth table uniqueness upper bound verify words XYZ is isosceles