How to prove it : a structured approach / [print]
Daniel J. Velleman.
- second edition.
- New York : Cambridge University Press, (c)2006.
- xiii, 384 pages : illustrations ; 24 cm.
Includes bibliographies and index.
Introduction -- Sentential logic -- 1.1 Deductive reasoning and logical connectives -- 1.2 truth tables -- 1.3 variables and sets -- 1.4 operations on sets -- 1.5 The conditional and biconditional connectives -- Quantificational logic -- 2.1 Quantifiers -- 2.2 Equivalences involving quantifiers -- 2.3 More operations on sets -- Proofs -- 3.1 proof strategies -- 3.2 proofs involving negations and conditionals -- 3.3 Proofs involving quantifiers -- 3.4 Proofs involving conjunctions and biconditionals -- 3.5 Proofs involving disjunctions -- 3.6 Existence and uniqueness proofs -- 3.7 More examples of proofs -- Relations -- 4.1 Ordered pairs and cartesian products -- 4.2 Relations -- 4.3 More about relations -- 4.4 Ordering relations -- 4.5 Closures -- 4.6 Equivalence relations -- Functions -- 5.1 Functions -- 5.2 One-to-one and onto -- 5.3 Inverses of functions -- 5.4 Images and inverse images: a research project -- Mathematical induction -- 6.1 Proof by mathematical induction -- 6.2 More examples -- 6.3 Recursion -- 6.4 Strong induction -- 6.5 Closures again -- Infinite sets -- 7.1 Equinumerous sets -- 7.2 Countable and uncountable sets -- 7.3 The cantor--Schroder--Bernstein theorem -- Appendix 1: Solutions to selected exercises -- Appendix 2: Proof designer -- Suggestions for further reading -- Summary for proof techniques -- Index.