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Contents Embed Dark Mode Prev Up Next \(\newcommand{\N}{\mathbb N}
\newcommand{\Z}{\mathbb Z}
\newcommand{\Q}{\mathbb Q}
\newcommand{\R}{\mathbb R}
\newcommand{\C}{\mathbb C}
\newcommand{\bC}{\mathbb C}
\newcommand{\st}{~:~}
\newcommand{\inv}{^{-1}}
\newcommand{\s}{\varrho}
\newcommand{\lt}{<}
\newcommand{\gt}{>}
\newcommand{\amp}{&}
\definecolor{fillinmathshade}{gray}{0.9}
\newcommand{\fillinmath}[1]{\mathchoice{\colorbox{fillinmathshade}{$\displaystyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\textstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptscriptstyle\phantom{\,#1\,}$}}}
\)
Handout Same or different?
Below are a collection of group tables for some of the groups we have encountered in this course. There is just one question: How many different groups are on this page?
\(\cdot\) (1)
(123)
(132)
(12)
(13)
(23)
(1)
(1)
(123)
(132)
(12)
(13)
(23)
(123)
(123)
(132)
(1)
(13)
(23)
(12)
(132)
(132)
(1)
(123)
(23)
(12)
(13)
(12)
(12)
(23)
(13)
(1)
(132)
(123)
(13)
(13)
(12)
(23)
(123)
(1)
(132)
(23)
(23)
(13)
(12)
(132)
(123)
(1)
\(\cdot\) ⚝
🍄
🐧
🞛
🙂
⛏
⚝
⚝
🍄
🐧
🞛
🙂
⛏
🍄
🍄
⚝
🞛
🐧
⛏
🙂
🐧
🐧
⛏
🙂
🍄
⚝
🞛
🞛
🞛
🙂
⛏
⚝
🍄
🐧
🙂
🙂
🞛
⚝
⛏
🐧
🍄
⛏
⛏
🐧
🍄
🙂
🞛
⚝
\(+\) (0,0)
(0,1)
(1,0)
(1,1)
(0,0)
(0,0)
(0,1)
(1,0)
(1,1)
(0,1)
(0,1)
(0,0)
(1,1)
(1,0)
(1,0)
(1,0)
(1,1)
(0,0)
(0,1)
(1,1)
(1,1)
(1,0)
(0,1)
(0,0)
\(+\) 0
1
2
3
0
0
1
2
3
1
1
2
3
0
2
2
3
0
1
3
3
0
1
2
\(\ast\) \(e\) \(a\) \(b\) \(d\)
\(e\) \(e\) \(a\) \(b\) \(d\)
\(a\) \(a\) \(b\) \(d\) \(e\)
\(b\) \(b\) \(d\) \(e\) \(a\)
\(d\) \(d\) \(e\) \(a\) \(b\)
\(\ast\) \(e\) \(a\) \(b\) \(d\)
\(e\) \(e\) \(a\) \(b\) \(d\)
\(a\) \(a\) \(d\) \(e\) \(b\)
\(b\) \(b\) \(e\) \(d\) \(a\)
\(d\) \(d\) \(b\) \(a\) \(e\)
\(+\) \(0+\langle 4\rangle\) \(1+\langle 4\rangle\) \(2+\langle 4\rangle\) \(3+\langle 4\rangle\)
\(0+\langle 4\rangle\) \(0+\langle 4\rangle\) \(1+\langle 4\rangle\) \(2+\langle 4\rangle\) \(3+\langle 4\rangle\)
\(1+\langle 4\rangle\) \(1+\langle 4\rangle\) \(2+\langle 4\rangle\) \(3+\langle 4\rangle\) \(0+\langle 4\rangle\)
\(2+\langle 4\rangle\) \(2+\langle 4\rangle\) \(3+\langle 4\rangle\) \(0+\langle 4\rangle\) \(1+\langle 4\rangle\)
\(3+\langle 4\rangle\) \(3+\langle 4\rangle\) \(0+\langle 4\rangle\) \(1+\langle 4\rangle\) \(2+\langle 4\rangle\)
It depends on what the mean of the word “is” is.
―Bill Clinton
