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mark 2023-10-10 17:34:45 -07:00
parent a536a31f2a
commit ce68014eec
2 changed files with 3 additions and 3 deletions
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2
Advanced/Cryptography/parts/1 mod.tex
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@ -8,7 +8,7 @@ Create a multiplication table for $\mathbb{Z}_4$:
\begin{center} \begin{center}
\begin{tabular}{c | c c c c} \begin{tabular}{c | c c c c}
\times & 0 & 1 & 2 & 3 \\ $\times$ & 0 & 1 & 2 & 3 \\
\hline \hline
0 & ? & ? & ? & ? \\ 0 & ? & ? & ? & ? \\
1 & ? & ? & ? & ? \\ 1 & ? & ? & ? & ? \\

4
Advanced/Intro to Proofs/main.tex
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@ -220,10 +220,10 @@
Show that for any two functions $g: Y \to W$ and $h: Y \to W$, if Show that for any two functions $g: Y \to W$ and $h: Y \to W$, if
$g \circ f = h \circ f \implies g = h$. $g \circ f = h \circ f \implies g = h$.
\item[\star] Let $f: X \to Y$ be a function where for any set $Z$ and functions $g: Z \to X$ and $h: Z \to X$, \item[$\star$] Let $f: X \to Y$ be a function where for any set $Z$ and functions $g: Z \to X$ and $h: Z \to X$,
$f \circ g = f \circ h \implies g = h$. Show that $f$ is injective. $f \circ g = f \circ h \implies g = h$. Show that $f$ is injective.
\item[\star] Let $f: X \to Y$ be a function where for any set $W$ and functions $g: Y \to W$ and $h: Y \to W$, \item[$\star$] Let $f: X \to Y$ be a function where for any set $W$ and functions $g: Y \to W$ and $h: Y \to W$,
$g \circ f = h \circ f \implies g = h$. Show f is surjective. $g \circ f = h \circ f \implies g = h$. Show f is surjective.
\end{itemize} \end{itemize}