TableofContents

# TableofContents - Contents Chapter 1 Introduction to Sets and Functions 9 1 Introduction to Sets 9 1.1 Basic Terminology 9 1.2 Notation for

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Unformatted text preview: Contents Chapter 1. Introduction to Sets and Functions 9 1. Introduction to Sets 9 1.1. Basic Terminology 9 1.2. Notation for Describing a Set 9 1.3. Common Universal Sets 10 1.4. Complements and Subsets 11 1.5. Element v.s. Subsets 11 1.6. Cardinality 12 1.7. Set Operations 12 1.8. Example 1.8.1 13 1.9. Product 13 2. Introduction to Functions 15 2.1. Function 15 2.2. Terminology Related to Functions 16 2.3. Example 2.3.1 16 2.4. Floor and Ceiling Functions 17 2.5. Characteristic Function 19 Chapter 2. Logic 21 1. Logic Definitions 21 1.1. Propositions 21 1.2. Examples 21 1.3. Logical Operators 22 1.4. Negation 23 1.5. Conjunction 24 1.6. Disjunction 24 1.7. Exclusive Or 25 1.8. Implications 25 1.9. Terminology 26 1.10. Example 27 1.11. Biconditional 27 1.12. NAND and NOR Operators 28 1.13. Example 29 1.14. Bit Strings 31 2. Propositional Equivalences 33 2.1. Tautology/Contradiction/Contingency 33 3 CONTENTS 4 2.2. Logically Equivalent 34 2.3. Examples 35 2.4. Important Logical Equivalences 37 2.5. Simplifying Propositions 38 2.6. Implication 40 2.7. Normal or Canonical Forms 41 2.8. Examples 41 2.9. Constructing Disjunctive Normal Forms 42 2.10. Conjunctive Normal Form 43 3. Predicates and Quantifiers 45 3.1. Predicates and Quantifiers 45 3.2. Example of a Propositional Function 45 3.3. Quantifiers 46 3.4. Example 3.4.1 47 3.5. Converting from English 47 3.6. Additional Definitions 48 3.7. Examples 48 3.8. Multiple Quantifiers 49 3.9. Ordering Quantifiers 49 3.10. Unique Existential 51 3.11. De Morgan’s Laws for Quantifiers 52 3.12. Distributing Quantifiers over Operators3....
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## This note was uploaded on 11/27/2011 for the course MCH 108 taught by Professor Penelopekirby during the Fall '08 term at FSU.

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TableofContents - Contents Chapter 1 Introduction to Sets and Functions 9 1 Introduction to Sets 9 1.1 Basic Terminology 9 1.2 Notation for

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