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About this book :-
Boolean Algebra written by Reuben Goodstein .
The fifth and last chapter of this books is more important becuase in last chapter Boolean algebra is examined in the setting of the theory of partial order. The treatment is entirely elementary and my aim has been to use Boolean algebra as a simple medium for introducing important concepts of modern algebra.
Book Detail :-
Title: Boolean Algebra
Author(s): Reuben Louis Goodstein
Publisher: Dover Publications
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About Author :-
The author Reuben Louis Goodstein , University of Leicester.
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Book Contents :-
Boolean Algebra written by Reuben Goodstein cover the following topics.
1. The Informal Algebra of Classes
Union, intersection and complementation. The commutative, associative and distributive laws. Difference and symmetric difference. Venn diagrams. Examples I
2. The Self-Dual System of Axioms
Standard forms. Completeness of the axiom systems. Independence of the axioms. An algebra of pairs. Isomorphism and homomorphism. Examples II
3. Boolean Equations
A bi-operational system of axioms. Equivalence of the two formalizations. The general solutions of Boolean equations. Congruence relations. Independence of the axioms. Examples III
4. Sentence Logic
Sentence logic as a model of Boolean algebra. The third system of axioms. Truth-table completeness. Independence of the axioms. The deduction theorem. Examples IV
Partially ordered sets. Atoms, minimal and maximal elements. Upper and lower bounds. Distributive lattices. Complemented distributive lattices. Union and intersection ideals. The lattice of union ideals. Representation theorems for Boolean algebras. A denumerable Boolean algebra. Newman algebra. Examples V
Solutions to Examples