TY  - BOOK
AU  - Velleman,Daniel J
TI  - How to prove it: a structured approach 
SN  - 9780521675994
AV  - QA9 
PY  - 2006///
CY  - New York
PB  - Cambridge University Press
KW  - Logic, Symbolic and mathematical
KW  - Mathematics
N1  - 2; 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; 2
ER  -