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# Logic and Boolean Algebra

• 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 Bn
• 3-5 Connection with Logic
• 4 Lattices
• 4-1 Introduction
• 4-2 Basic Definitions
• 4-3 Further Properties of Lattices
• 4-4 The Lattice Bn 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 Bn 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 Bn
• 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