Logic and discrete mathematics : a concise introduction / / Willem Conradie, Valentin Goranko

• Autore: Conradie Willem <1978->
• Pubblicazione: West Sussex, England : , : Wiley, , 2015; ©2015
• Descrizione fisica: 1 online resource (452 p.)
• Disciplina: 511.3
• Soggetto topico: Logic, Symbolic and mathematical; Computer science - Mathematics
• Soggetto genere / forma: Electronic books.
• Persona (resp. second.): GorankoValentin
• Note generali: Includes index.
• Nota di contenuto: Cover; Title Page; Copyright; Contents; List of Boxes; Preface; Acknowledgements; About the Companion Website; Chapter 1 Preliminaries; 1.1 Sets; 1.1.1 Exercises; 1.2 Basics of logical connectives and expressions; 1.2.1 Propositions, logical connectives, truth tables, tautologies; 1.2.2 Individual variables and quantifiers; 1.2.3 Exercises; 1.3 Mathematical induction; 1.3.1 Exercises; Chapter 2 Sets, Relations, Orders; 2.1 Set inclusions and equalities; 2.1.1 Properties of the set theoretic operations; 2.1.2 Exercises; 2.2 Functions; 2.2.1 Functions and their inverses ; 2.2.2 Composition of mappings2.2.3 Exercises; 2.3 Binary relations and operations on them; 2.3.1 Binary relations; 2.3.2 Matrix and graphical representations of relations on finite sets; 2.3.3 Boolean operations on binary relations; 2.3.4 Inverse and composition of relations; 2.3.5 Exercises; 2.4 Special binary relations; 2.4.1 Properties of binary relations; 2.4.2 Functions as relations; 2.4.3 Reflexive, symmetric and transitive closures of a relation; 2.4.4 Exercises; 2.5 Equivalence relations and partitions; 2.5.1 Equivalence relations; 2.5.2 Quotient sets and partitions ; 2.5.3 The kernel equivalence of a mapping2.5.4 Exercises; 2.6 Ordered sets; 2.6.1 Pre-orders and partial orders; 2.6.2 Graphical representing posets: Hasse diagrams; 2.6.3 Lower and upper bounds. Minimal and maximal elements; 2.6.4 Well-ordered sets; 2.6.5 Exercises; 2.7 An introduction to cardinality; 2.7.1 Equinumerosity and cardinality; 2.7.2 Exercises; 2.8 Isomorphisms of ordered sets. Ordinal numbers; 2.8.1 Exercises; 2.9 Application: relational databases; 2.9.1 Exercises; Chapter 3 Propositional Logic; 3.1 Propositions, logical connectives, truth tables, tautologies ; 3.1.1 Propositions and propositional connectives. Truth tables3.1.2 Some remarks on the meaning of the connectives; 3.1.3 Propositional formulae; 3.1.4 Construction and parsing tree of a propositional formula; 3.1.5 Truth tables of propositional formulae; 3.1.6 Tautologies; 3.1.7 A better idea: search for a falsifying truth assignment; 3.1.8 Exercises; 3.2 Propositional logical consequence. Valid and invalid propositional inferences; 3.2.1 Propositional logical consequence; 3.2.2 Logically sound rules of propositional inference. Logically correct propositional arguments ; 3.2.3 Fallacies of the implication3.2.4 Exercises; 3.3 The concept and use of deductive systems; 3.4 Semantic tableaux; 3.4.1 Exercises; 3.5 Logical equivalences. Negating propositional formulae; 3.5.1 Logically equivalent propositional formulae; 3.5.2 Some important equivalences; 3.5.3 Exercises; 3.6 Normal forms. Propositional resolution; 3.6.1 Conjunctive and disjunctive normal forms of propositional formulae; 3.6.2 Clausal form. Clausal resolution; 3.6.3 Resolution-based derivations; 3.6.4 Optimizing the method of resolution; 3.6.5 Exercises; Chapter 4 First-Order Logic ; 4.1 Basic concepts of first-order logic
• Sommario/riassunto: A concise yet rigorous introduction to logic and discrete mathematics. This book features a unique combination of comprehensive coverage of logic with a solid exposition of the most important fields of discrete mathematics, presenting material that has been tested and refined by the authors in university courses taught over more than a decade. The chapters on logic - propositional and first-order - provide a robust toolkit for logical reasoning, emphasizing the conceptual understanding of the language and the semantics of classical logic as well as practical applications through the easy
• Titolo autorizzato: Logic and discrete mathematics
• ISBN: 1-118-76109-X
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910460966303321
• Lo trovi qui: Univ. Federico II