Logic and Set Theory

Abstract

This chapter presents some of the fundamental ideas of logic and set theory and establishes the notation that is to be used subsequently. “Statement” means a declarative, meaningful sentence or phrase in grammatically correct English, which is capable of having assigned to it one truth value, true (T) or false (F). Closely related to the concept of statement is that of an open sentence, or statement function. It means a collection of words and symbols, the latter called variables, which becomes a statement when each variable is replaced by a certain object. Some symbols stand for variables and others do not. In addition to the device of substituting specific items for variables, there is another way to make statements from open sentences; this process is called quantification. The chapter discusses two prefix-like symbols, called quantifiers: the universal quantifier, and the existential quantifier. There is a treatment of set theory in which sets are defined in terms of more primitive things.