How to prove it
Subtitle: a structured approach
By: Daniel J. Velleman.
Edition: 2nd ed.
Publisher: Cambridge University Press
Published: 2006
Place of publication: New York
Language: eng
Number of pages: 400
ISBN-13: 9780521861243; 9780521675994
Subjects: Logic, Symbolic and mathematical.; Mathematics.
Notes: Includes bibliographical references and index.
Table of contents: title: Introduction; title: Sentential logic; title: 1.1 Deductive reasoning and logical connectives; title: 1.2 truth tables; title: 1.3 variables and sets; title: 1.4 operations on sets; title: 1.5 The conditional and biconditional connectives; title: Quantificational logic; title: 2.1 Quantifiers; title: 2.2 Equivalences involving quantifiers; title: 2.3 More operations on sets; title: Proofs; title: 3.1 proof strategies; title: 3.2 proofs involving negations and conditionals; title: 3.3 Proofs involving quantifiers; title: 3.4 Proofs involving conjunctions and biconditionals; title: 3.5 Proofs involving disjunctions; title: 3.6 Existence and uniqueness proofs; title: 3.7 More examples of proofs; title: Relations; title: 4.1 Ordered pairs and cartesian products; title: 4.2 Relations; title: 4.3 More about relations; title: 4.4 Ordering relations; title: 4.5 Closures; title: 4.6 Equivalence relations; title: Functions; title: 5.1 Functions; title: 5.2 One-to-one and onto; title: 5.3 Inverses of functions; title: 5.4 Images and inverse images: a research project; title: Mathematical induction; title: 6.1 Proof by mathematical induction; title: 6.2 More examples; title: 6.3 Recursion; title: 6.4 Strong induction; title: 6.5 Closures again; title: Infinite sets; title: 7.1 Equinumerous sets; title: 7.2 Countable and uncountable sets; title: 7.3 The cantor; title: Schroder; title: Bernstein theorem; title: Appendix 1: Solutions to selected exercises; title: Appendix 2: Proof designer; title: Suggestions for further reading; title: Summary for proof techniques; title: Index.