Some Other Methods of Proof

$\newcommand{\N}{\mathbb N} \newcommand{\Z}{\mathbb Z} \newcommand{\Q}{\mathbb Q} \newcommand{\R}{\mathbb R} \newcommand{\M}{\mathcal M} \newcommand{\modulo}[3]{#1 \equiv #2 \pmod #3} \newcommand{\notmodulo}[3]{#1 \not \equiv #2 \pmod #3} \newcommand{\abs}[1]{\left| #1 \right|} \newcommand{\dom}[1]{\text{ dom} ( #1 )} \newcommand{\codom}[1]{\text{ codom} ( #1 )} \newcommand{\range}[1]{\text{ range} ( #1 )} \newcommand{\lt}{<} \newcommand{\gt}{>} \newcommand{\amp}{&} \definecolor{fillinmathshade}{gray}{0.9} \newcommand{\fillinmath}[1]{\mathchoice{\colorbox{fillinmathshade}{$\displaystyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\textstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptscriptstyle\phantom{\,#1\,}$}}} $

Chapter 3 Some Other Methods of Proof

It is sometimes difficult to construct a direct proof of a conditional statement. Fortunately, there are certain logical equivalencies in Theorem 1.1 that can be used to justify some other methods of proof of a conditional statement. Knowing that two expressions are logically equivalent tells us that if we prove one, then we have also proven the other. In fact, once we know the truth value of a statement, then we know the truth value of any other statement that is logically equivalent to it.

Constructing and Writing Mathematical Proofs: A Guide for Mathematics Students

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Chapter 3 Some Other Methods of Proof