One of 12 books developed for use with the core material (Book O) of the Elements of Mathematics Program, this text covers material well beyond the scope of the usual secondary mathematics sequences. These materials are designed for highly motivated students with strong verbal abilities; mathematical theories and ideas are developed through problem situations and explanatory materials. This volume begins with a discussion of infinite sets; basic set theory, introduced in Book O, is reviewed and extended. Set builder notation is used in conjunction with logical connectives. The empty set and universal set are discussed. Many theorems are proved. (SD)