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Logic for Linear Algebraists:
150 minutes of logic for proof writing
Courtney R. Gibbons
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\(\newcommand{\NN}{\mathbb N} \newcommand{\ZZ}{\mathbb Z} \newcommand{\QQ}{\mathbb Q} \newcommand{\RR}{\mathbb R} \newcommand{\lt}{<} \newcommand{\gt}{>} \newcommand{\amp}{&} \definecolor{fillinmathshade}{gray}{0.9} \newcommand{\fillinmath}[1]{\mathchoice{\colorbox{fillinmathshade}{$\displaystyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\textstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptscriptstyle\phantom{\,#1\,}$}}} \)
Front Matter
Acknowledgements
Colophon
Introduction
1
Connectives
1.1
First Connectives: Not, And, and Or
1.2
Compound Statements
1.3
Conditional and Biconditional Statements
1.4
Exercises
2
Quantifiers
2.1
Propositional Functions
2.2
Exercises
3
Proof Techniques
3.1
Direct Proofs
3.2
Indirect Proofs
3.2.1
Proof by Contrapositive
3.2.2
Proof by Contradiction
3.2.3
Other Logical Equivalences
3.3
Counterexamples
3.4
Exercises
4
Challenging Exercises
Backmatter
A
Style Conventions for Formal Mathematical Writing
A.1
Logic
A.2
Mathematics
A.3
Style
A.4
Examples (and how to write them)
B
Sets
B.1
Functions
B.1
Exercises
B.2
Equivalence relations on sets
Colophon
Colophon
Colophon
This book was authored in PreTeXt.
