The purpose of this chapter is not to present a complete account of symbolic logic, but rather to introduce the subject in a way which will prepare the student for the task of reading a more comprehensive work. In addition to laying a background for further study, this chapter will present enough of the basic ideas of symbolic logic to give an appreciation of the role the subject plays in mathematics, and to illustrate that the algebra of logic is another example of a Boolean algebra.  Logic is an extensive field of study with many special areas of inquiry.  In general, logic is concerned with the study and analysis of methods of reasoning or argumentation. Symbolic logic is not precisely defined as distinct from logic in general, but might be described as a study of logic which employs an extensive use of symbols.

In any discussion of logic, the treatment centers around the concept of a proposition (statement). The principal tool for treatment of propositions is the algebra of propositions, a Boolean algebra. In talking about propositions, we will also investigate certain logical forms which representacceptable techniques for constructing precise proofs of theorems. Since statements are formed from words, it is apparent that some considerationmust be given to words and their meanings. No logical argument can be based on words that are not precisely described. That part of logic whichis concerned with the structure of statements is much more difficult than the areas mentioned previously, and in fact, has not been satisfactorily formalized. We will limit our attention to a few types of sentence construction that are of special interest in the formulation of mathematical statements.

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