ABSTRACT
Mathematical reasoning and arguments are based on the rules of logic. This chapter explores how to prove statements. It provides a discussion of software implementation of sets. The notation that needs to be introduced is primarily set notation. It is considered in a more precise way after logic and quantifiers are formally established. A helpful way to visualize the set operations is provided by Venn diagrams, in which sets are represented by enclosed regions. If set-like data structures are needed in computer software, then certainly basic operations like union, intersection, and difference are also needed to manipulate these structures. As a closely related application, the chapter considers digital circuits, since their underlying structure is the same as that of statements. A statement may involve multiple quantifiers and, consequently, multiple bound variables. The chapter lists some of the basic logical equivalences that can be used to construct others. Logical equivalences are useful for manipulating and simplifying logical expressions.
