An intuitive approach to the algebra of sets was followed in (THE ALGEBRA OF SETS) in order to make the introduction to Boolean algebra as intuitive and natural as possible. All three of the applications of Boolean algebra mentioned in this book are readily treated in an elementary manner.

However, to discuss each entirely separately, with separate proofs of all important theorems, is a needless waste of time. In addition, such a treatment would tend to emphasize the dissimilarities between the applications rather than their essential unity. For this reason, among others, the present chapter presents a treatment of Boolean algebras in general,  based on a set of definitions and axioms from which all subsequent theorems are derived. There will be . ome duplication of the material introduced in  (THE ALGEBRA OF SETS), of course, but whereas the results of (THE ALGEBRA OF SETS) were based on intuitive concepts and applied only to sets, results in this chapter are derived in a rigorous manner, and apply equally well in every Boolean algebra.

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

THE ALGEBRA OF SETS-Introduction