Boolean algebra, as the name suggests, is part of that branch of mathematics known as modern algebra, or abstract algebra.

It is one of the most easily understood of the algebraic systems usually studied in a basic course in algebra because of its simplicity and because of the readily available applications to illustrate the theory. No particular subject matter is prerequisite to the study of this text, although any maturity gained in other mathematics courses will be helpful.

In order to present Boolean algebra in a way which can be readily followed by a beginner, this chapter deals only with one of the special examples of a Boolean algebra, the algebra of sets. This example was chosen because it is perhaps the most intuitive of all applications and because at the same time it is complex enough to reveal the essential nature of any Boolean algebra. The development is entirely intuitive, in that any proofs given are based on intuitive concepts rather than on formal axioms. The axiomatic approach is delayed until BOOLEAN ALGEBRA.

While this order is perhaps less satisfying to a professional mathematician,  it is hoped that a greater appreciation of the precise formulation will result because the reader is already familiar with the properties represented in the axioms.

مواضيع ذات صلة

Zero Polynomial

Kronecker,s Polynomial Theorem

THE ALGEBRA OF SETS-The number of elements in a set

THE ALGEBRA OF SETS-Solution of equations

THE ALGEBRA OF SETS-Conditional equations

THE ALGEBRA OF SETS-Properties of set inclusion

THE ALGEBRA OF SETS- Expanding, factoring, and simplifying

THE ALGEBRA OF SETS-Fundamental laws

THE ALGEBRA OF SETS-Venn diagrams

THE ALGEBRA OF SETS-The combination of sets

THE ALGEBRA OF SETS-Element and set

SYMBOLIC LOGIC AND THE ALGEBRA OF PROPOSITIONS-Special problems