Learning to Reason: An Introduction to Logic, Sets, and Relations / Edition 1

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Learn how to develop your reasoning skills and how to write well-reasoned proofs

Learning to Reason shows you how to use the basic elements of mathematical language to develop highly sophisticated, logical reasoning skills. You'll get clear, concise, easy-to-follow instructions on the process of writing proofs, including the necessary reasoning techniques and syntax for constructing well-written arguments. Through in-depth coverage of logic, sets, and relations, Learning to Reason offers a meaningful, integrated view of modern mathematics, cuts through confusing terms and ideas, and provides a much-needed bridge to advanced work in mathematics as well as computer science. Original, inspiring, and designed for maximum comprehension, this remarkable book:
* Clearly explains how to write compound sentences in equivalent forms and use them in valid arguments
* Presents simple techniques on how to structure your thinking and writing to form well-reasoned proofs
* Reinforces these techniques through a survey of sets—the building blocks of mathematics
* Examines the fundamental types of relations, which is "where the action is" in mathematics
* Provides relevant examples and class-tested exercises designed to maximize the learning experience
* Includes a mind-building game/exercise space at www.wiley.com/products/subject/mathematics/

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Editorial Reviews

From the Publisher
"A primary strength is its broad attention to ideas from logic, settheory and relations while focusing the key notions of symbolismand writing proofs." (Choice, Vol. 38, No. 7, March 2001)

"In this textbook for mathematics and computer science majors,Rodgers explains how to write compound sentences in equivalentforms and use them in valid arguments..." (SciTech Book News, March2001)

A primary strength is its broad attention to ideas from logic, set theory and relations while focusing the key notions of symbolism and writing proofs.
SciTech Book News
In this textbook for mathematics and computer science majors, Rodgers explains how to write compound sentences in equivalent forms and use them in valid arguments...
In this textbook for mathematics and computer science majors, Rodgers (Hanover College) explains how to write compound sentences in equivalent forms and use them in valid arguments, and how to structure thinking and writing to form well-reasoned proofs before moving on to mathematical sets and relations. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9780471371229
  • Publisher: Wiley
  • Publication date: 7/20/2000
  • Edition number: 1
  • Pages: 454
  • Product dimensions: 7.68 (w) x 9.57 (h) x 1.07 (d)

Meet the Author

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

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Table of Contents


Symbolic Language.

Two Quantifiers.

Five Logical Operators.

Laws of Logic.

Logic Circuits.



Proofs and Arguments.

Proving Implications.

Writing a Proof.

Working with Quantifiers.

Using Cases.

Proof by Contradiction.

Mathematical Induction.

Axiomatic Systems.


Sets and Elements.

Operations on Sets.

Multiple Unions and Intersections.

Cross Product.

Finite Sets.

Infinite Sets.



Equivalence Relations.


Order Relations.




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