College Math

College Math Study Guide

Chapter 6: Logic and Sets Overview Studying logic and set theory are vital aspect of mathematics, as they provide a structure and foundation to the number systems used in both mathematics and everyday life. This chapter will introduce you to the basic concepts, symbols, and importance of studying sets and theory. The set theory aims to explain how basic as well as compound statements with nouns and predicates are formulated in an abstract language like mathematics. Further, when the set theory is combined with logic, it provides foundation for the entire mathematics. In this chapter, you will learn the basics of logics, logical statements and operations, symbols, truth values and truth tables, conditional statements, logical equivalence, logical arguments, and a few other important concepts. Further, the concept building and application of sets and set theory has been briefed. Objectives By the end of the chapter, you will be able to understand: • Meaning, usage, and importance of logical statements • Solving logical operations and statements • Representing, deriving, and solving logical statements • Logical arguments, conditional statements, and logical equivalence • Importance and basics of set theory • Operations on sets 6.1 Logical Operations and Statements Symbolic logic represents the parts of natural language using symbols. We make use of statements and connectives when we talk about logics. Statements are simple assertions that can be true or false. For instance- ‘ It will rain today’ is a simple statement. Statements are generally represented by small alphabetical letters. Connectives join together different simple statements and make them compound statements. Connectives are used in the cases when the statements make use of words like ‘and, or, implies.’

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