05416nam 2200685 450 991046096630332120210616123819.01-118-76109-X(CKB)3710000000400815(EBL)1895582(SSID)ssj0001459329(PQKBManifestationID)11746594(PQKBTitleCode)TC0001459329(PQKBWorkID)11457377(PQKB)11020399(PQKBManifestationID)16040129(PQKB)23666690(MiAaPQ)EBC1895582(DLC) 2014036104(PPN)224232177(Au-PeEL)EBL1895582(CaPaEBR)ebr11048164(CaONFJC)MIL776647(OCoLC)908080251(EXLCZ)99371000000040081520150512h20152015 uy 0engur|n|---|||||txtccrLogic and discrete mathematics a concise introduction /Willem Conradie, Valentin GorankoWest Sussex, England :Wiley,2015.©20151 online resource (452 p.)Includes index.1-119-00009-2 1-118-75127-2 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 inverses2.2.2 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 partitions2.5.3 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, tautologies3.1.1 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 arguments3.2.3 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 Logic4.1 Basic concepts of first-order logicA 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 easyLogic, Symbolic and mathematicalTextbooksComputer scienceMathematicsTextbooksElectronic books.Logic, Symbolic and mathematicalComputer scienceMathematics511.3Conradie Willem1978-918556Goranko ValentinMiAaPQMiAaPQMiAaPQBOOK9910460966303321Logic and discrete mathematics2059714UNINA