Nancy Rodgers 
Learning to Reason 
An Introduction to Logic, Sets, and Relations

Learn how to develop your reasoning skills and how to writewell-reasoned proofs

Learning to Reason shows you how to use the basic elements ofmathematical language to develop highly sophisticated, logicalreasoning skills. You’ll get clear, concise, easy-to-followinstructions on the process of writing proofs, including thenecessary reasoning techniques and syntax for constructingwell-written arguments. Through in-depth coverage of logic, sets, and relations, Learning to Reason offers a meaningful, integratedview of modern mathematics, cuts through confusing terms and ideas, and provides a much-needed bridge to advanced work in mathematicsas well as computer science. Original, inspiring, and designed formaximum comprehension, this remarkable book:

* Clearly explains how to write compound sentences in equivalentforms and use them in valid arguments

* Presents simple techniques on how to structure your thinking andwriting to form well-reasoned proofs

* Reinforces these techniques through a survey of sets–thebuilding blocks of mathematics

* Examines the fundamental types of relations, which is ‘where theaction is’ in mathematics

* Provides relevant examples and class-tested exercises designed tomaximize the learning experience

* Includes a mind-building game/exercise space atwww.wiley.com/products/subject/mathematics/

Table of Content

LOGICAL REASONING.

Symbolic Language.

Two Quantifiers.

Five Logical Operators.

Laws of Logic.

Logic Circuits.

Translations.

WRITING OUR REASONING.

Proofs and Arguments.

Proving Implications.

Writing a Proof.

Working with Quantifiers.

Using Cases.

Proof by Contradiction.

Mathematical Induction.

Axiomatic Systems.

SETS –

THE BUILDING BLOCKS.

Sets and Elements.

Operations on Sets.

Multiple Unions and Intersections.

Cross Product.

Finite Sets.

Infinite Sets.

RELATIONS –

THE ACTION.

Relations.

Equivalence Relations.

Functions.

Order Relations.

Summary.

Appendices.

Bibliography.

About the author

NANCY RODGERS, Ph D, is Professor of Mathematics at Hanover College, Hanover, Indiana.