Skip to main content\(\newcommand{\N}{\mathbb N}
\newcommand{\Z}{\mathbb Z}
\newcommand{\R}{\mathbb R}
\newcommand{\Q}{\mathbb Q}
\newcommand{\mynot}{\neg}
\newcommand{\card}{\mathbf{card}}
\newcommand{\x}{:}
\newcommand{\Mod}[1]{\ (\mathrm{mod}\ #1)}
\DeclarePairedDelimiter\abs{\lvert}{\rvert}
\newcommand{\lt}{<}
\newcommand{\gt}{>}
\newcommand{\amp}{&}
\definecolor{fillinmathshade}{gray}{0.9}
\newcommand{\fillinmath}[1]{\mathchoice{\colorbox{fillinmathshade}{$\displaystyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\textstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptscriptstyle\phantom{\,#1\,}$}}}
\)
Beginning Activity Beginning Activity 2: Equivalent Sets, Part 2
1.
Review Theorem 6.29 in Section 6.4, Theorem 6.36 in Section 6.5, and Exercise 9 in Section 6.5.
2.
Prove each part of the following theorem.
Theorem 9.1.
Let \(A\text{,}\) \(B\text{,}\) and \(C\) be sets.
For each set \(A\text{,}\) \(A \approx A\text{.}\)
For all sets \(A\) and \(B\text{,}\) if \(A \approx B\text{,}\) then \(B \approx A\text{.}\)
For all sets \(A\text{,}\) \(B\text{,}\) and \(C\text{,}\) if \(A \approx B\) and \(B \approx C\text{,}\) then \(A \approx C\text{.}\)