Concise introduction to logic and set theory:
This book deals with two important branches of mathematics, namely, logic and set theory. Logic and set theory are closely related and play very crucial roles in the foundation of mathematics, and together produce several results in all of mathematics. The topics of logic and set theory are required...
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton ; London ; New York
CRC Press, Taylor & Francis Group
2022
|
| Ausgabe: | First edition |
| Schriftenreihe: | Mathematics and its applications: Modelling, engineering, and social sciences
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | This book deals with two important branches of mathematics, namely, logic and set theory. Logic and set theory are closely related and play very crucial roles in the foundation of mathematics, and together produce several results in all of mathematics. The topics of logic and set theory are required in many areas of physical sciences, engineering, and technology. The book offers solved examples and exercises, and provides reasonable details to each topic discussed, for easy understanding. The book is designed for readers from various disciplines where mathematical logic and set theory play a crucial role. The book will be of interested to students and instructors in engineering, mathematics, computer science, and technology |
| Beschreibung: | Preface; About Authors; 1. Mathematical Logic; 2. Set Theory; 3. Relations; 4. Functions; 5. Cardinality of Sets; Bibliography; Index |
| Beschreibung: | ix, 160 Seiten Illustrationen 472 grams |
| ISBN: | 9780367077952 9781032106229 |
Internformat
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| 245 | 1 | 0 | |a Concise introduction to logic and set theory |c Iqbal H. Jebril, Hemen Dutta, and Ilwoo Cho |
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| 500 | |a Preface; About Authors; 1. Mathematical Logic; 2. Set Theory; 3. Relations; 4. Functions; 5. Cardinality of Sets; Bibliography; Index | ||
| 520 | |a This book deals with two important branches of mathematics, namely, logic and set theory. Logic and set theory are closely related and play very crucial roles in the foundation of mathematics, and together produce several results in all of mathematics. The topics of logic and set theory are required in many areas of physical sciences, engineering, and technology. The book offers solved examples and exercises, and provides reasonable details to each topic discussed, for easy understanding. The book is designed for readers from various disciplines where mathematical logic and set theory play a crucial role. The book will be of interested to students and instructors in engineering, mathematics, computer science, and technology | ||
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Datensatz im Suchindex
| _version_ | 1822603488801062912 |
|---|---|
| adam_text |
Contents Preface.vii About Authors.ix Chapter 1 Mathematical Logic.1 1.1 1.2 1.3 1.4 1.5 1.6 Sets. 1 Propositions and Connectives. 3 Tautology and Contradiction.10 Quantifiers. 12 Logical Reasoning.16 Mathematical Proof.18 1.6.1 Direct and contrapositive Proof.18 1.6.2 Contradiction Proof. 20 1.7 Induction.23 1.7.1 Introduction. 23 1.7.2 Induction Principle. 24 Chapter 2 Set Theory. 29 2.1 Basic Notions of Set Theory. 29 2.2 Elementary Properties of Sets. 32 2.2.1 Union of
Sets. 32 2.2.2 Intersection of Sets. 34 2.2.3 Complement of Set. 39 2.2.4 Difference and Symmetric Difference of Sets.42 2.3 Indexed Families of Sets. 45 Chapter 3 Relations. 51 3.1 Ordered Pairs and Cartesian Product. 51 3.2 Relations on Sets. 56 3.3 Type of Relations. 66 3.4 Equivalence Relations and Equivalence Classes.70 3.5 Congruence.76 3.6 Partial and Total Ordered Relations. 83 Chapter 4 Functions. 97 4.1 Functions.97 4.1.1 Domain and Range. 97 v
vi Contents 4.2 4.3 4.4 Chapter 5 4.1.2 Graph of a Function. 99 One-to-one Functions and Onto Functions.101 Composite Functions and Inverse Functions.114 Direct Images and Inverse Images under a Function. 125 Cardinality of Sets.133 5.1 Cardinal Number. 133 5.1.1 Equipotent Sets.133 5.1.2 Countable Sets.140 5.1.3 Cardinal Arithmetic.144 5.1.4 Order Types.150 5.1.5 More About Cardinal Numbers.151 5.2 Axiom of Choice.154 Bibliography.і. 157 Index, 159 |
| adam_txt |
Contents Preface.vii About Authors.ix Chapter 1 Mathematical Logic.1 1.1 1.2 1.3 1.4 1.5 1.6 Sets. 1 Propositions and Connectives. 3 Tautology and Contradiction.10 Quantifiers. 12 Logical Reasoning.16 Mathematical Proof.18 1.6.1 Direct and contrapositive Proof.18 1.6.2 Contradiction Proof. 20 1.7 Induction.23 1.7.1 Introduction. 23 1.7.2 Induction Principle. 24 Chapter 2 Set Theory. 29 2.1 Basic Notions of Set Theory. 29 2.2 Elementary Properties of Sets. 32 2.2.1 Union of
Sets. 32 2.2.2 Intersection of Sets. 34 2.2.3 Complement of Set. 39 2.2.4 Difference and Symmetric Difference of Sets.42 2.3 Indexed Families of Sets. 45 Chapter 3 Relations. 51 3.1 Ordered Pairs and Cartesian Product. 51 3.2 Relations on Sets. 56 3.3 Type of Relations. 66 3.4 Equivalence Relations and Equivalence Classes.70 3.5 Congruence.76 3.6 Partial and Total Ordered Relations. 83 Chapter 4 Functions. 97 4.1 Functions.97 4.1.1 Domain and Range. 97 v
vi Contents 4.2 4.3 4.4 Chapter 5 4.1.2 Graph of a Function. 99 One-to-one Functions and Onto Functions.101 Composite Functions and Inverse Functions.114 Direct Images and Inverse Images under a Function. 125 Cardinality of Sets.133 5.1 Cardinal Number. 133 5.1.1 Equipotent Sets.133 5.1.2 Countable Sets.140 5.1.3 Cardinal Arithmetic.144 5.1.4 Order Types.150 5.1.5 More About Cardinal Numbers.151 5.2 Axiom of Choice.154 Bibliography.і. 157 Index, 159 |
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| discipline | Mathematik |
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| illustrated | Illustrated |
| index_date | 2024-07-03T18:36:05Z |
| indexdate | 2025-01-29T17:02:16Z |
| institution | BVB |
| isbn | 9780367077952 9781032106229 |
| language | English |
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| publishDate | 2022 |
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| publisher | CRC Press, Taylor & Francis Group |
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| spelling | Jebril, Iqbal H. ca. 20./21. Jh. Verfasser (DE-588)1257098381 aut Concise introduction to logic and set theory Iqbal H. Jebril, Hemen Dutta, and Ilwoo Cho First edition Boca Raton ; London ; New York CRC Press, Taylor & Francis Group 2022 ix, 160 Seiten Illustrationen 472 grams txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications: Modelling, engineering, and social sciences Preface; About Authors; 1. Mathematical Logic; 2. Set Theory; 3. Relations; 4. Functions; 5. Cardinality of Sets; Bibliography; Index This book deals with two important branches of mathematics, namely, logic and set theory. Logic and set theory are closely related and play very crucial roles in the foundation of mathematics, and together produce several results in all of mathematics. The topics of logic and set theory are required in many areas of physical sciences, engineering, and technology. The book offers solved examples and exercises, and provides reasonable details to each topic discussed, for easy understanding. The book is designed for readers from various disciplines where mathematical logic and set theory play a crucial role. The book will be of interested to students and instructors in engineering, mathematics, computer science, and technology bisacsh / TECHNOLOGY & ENGINEERING / Manufacturing bisacsh / MATHEMATICS / Set Theory Mathematische Logik (DE-588)4037951-6 gnd rswk-swf Mengenlehre (DE-588)4074715-3 gnd rswk-swf Mathematische Logik (DE-588)4037951-6 s Mengenlehre (DE-588)4074715-3 s DE-604 Dutta, Hemen 1981- Verfasser (DE-588)1138592625 aut Cho, Ilwoo ca. 20./21. Jh. Verfasser (DE-588)1257099051 aut Erscheint auch als Online-Ausgabe 978-0-429-02283-8 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032975869&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Jebril, Iqbal H. ca. 20./21. Jh Dutta, Hemen 1981- Cho, Ilwoo ca. 20./21. Jh Concise introduction to logic and set theory bisacsh / TECHNOLOGY & ENGINEERING / Manufacturing bisacsh / MATHEMATICS / Set Theory Mathematische Logik (DE-588)4037951-6 gnd Mengenlehre (DE-588)4074715-3 gnd |
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| title | Concise introduction to logic and set theory |
| title_auth | Concise introduction to logic and set theory |
| title_exact_search | Concise introduction to logic and set theory |
| title_exact_search_txtP | Concise introduction to logic and set theory |
| title_full | Concise introduction to logic and set theory Iqbal H. Jebril, Hemen Dutta, and Ilwoo Cho |
| title_fullStr | Concise introduction to logic and set theory Iqbal H. Jebril, Hemen Dutta, and Ilwoo Cho |
| title_full_unstemmed | Concise introduction to logic and set theory Iqbal H. Jebril, Hemen Dutta, and Ilwoo Cho |
| title_short | Concise introduction to logic and set theory |
| title_sort | concise introduction to logic and set theory |
| topic | bisacsh / TECHNOLOGY & ENGINEERING / Manufacturing bisacsh / MATHEMATICS / Set Theory Mathematische Logik (DE-588)4037951-6 gnd Mengenlehre (DE-588)4074715-3 gnd |
| topic_facet | bisacsh / TECHNOLOGY & ENGINEERING / Manufacturing bisacsh / MATHEMATICS / Set Theory Mathematische Logik Mengenlehre |
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