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Logic and Boolean Algebra

Table of Contents

• 1 Some Concepts of Intuitive Logic
  • 1-1 Introduction
  • 1-2 Sentences and Connectives
  • 1-3 Variables and Functions
  • 1-4 Related Sentential Functions; Truth Value Functions
  • 1-5 Some Methods of Proof
• 2 Boolean Functions
  • 2-1 Introduction
  • 2-2 Basic Definitions; Use of Tables
  • 2-3 Equivalence Relations
  • 2-4 Correspondence between Truth Value Functions and Boolean Functions
• 3 Ordered Sets
  • 3-1 Introduction
  • 3-2 Basic Definition; Graphical Representation
  • 3-3 Isomorphism
  • 3-4 The Ordering in B_n
  • 3-5 Connection with Logic
• 4 Lattices
  • 4-1 Introduction
  • 4-2 Basic Definitions
  • 4-3 Further Properties of Lattices
  • 4-4 The Lattice B_n and Applications to Logic
• 5 Boolean Algebras
  • 5-1 Introduction
  • 5-2 Basic Definition and Properties
  • 5-3 Representation in Terms of Subsets of a Set
  • 5-4 B_n as a Boolean Algebra; Applications to Logic
• 6 Boolean Rings
  • 6-1 Introduction
  • 6-2 Definitions and Basic Properties
  • 6-3 Boolean Rings with a Unit Element are Equivalent to Boolean Algebras
  • 6-4 Representation of a Finite Boolean Ring in Terms of n-tuples of Boolean Constants
• 7 Normal Forms, Duality
  • 7-1 Introduction
  • 7-2 Disjunctive and Conjunctive Normal Forms
  • 7-3 The Ring Normal Form
  • 7-4 Normal Forms in B_n
  • 7-5 Duality
• 8 Some Applications of Boolean Algebra
  • 8-1 Introduction
  • 8-2 Applications to Electrical Networks
  • 8-3 Applications to Computer Design
  • 8-4 Applications to Logic

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