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

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

by Nancy Rodgers
ISBN-10:
047137122X
ISBN-13:
9780471371229
Pub. Date:
07/20/2000
Publisher:
Wiley

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Overview

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

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/

Product Details

ISBN-13: 9780471371229
Publisher: Wiley
Publication date: 07/20/2000
Pages: 454
Product dimensions: 7.68(w) x 9.57(h) x 1.07(d)

Table of Contents

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.

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