diff --git a/Advanced/Cryptography/parts/1 mod.tex b/Advanced/Cryptography/parts/1 mod.tex index 5fa7786..5213b3d 100755 --- a/Advanced/Cryptography/parts/1 mod.tex +++ b/Advanced/Cryptography/parts/1 mod.tex @@ -8,7 +8,7 @@ Create a multiplication table for $\mathbb{Z}_4$: \begin{center} \begin{tabular}{c | c c c c} - \times & 0 & 1 & 2 & 3 \\ + $\times$ & 0 & 1 & 2 & 3 \\ \hline 0 & ? & ? & ? & ? \\ 1 & ? & ? & ? & ? \\ diff --git a/Advanced/Intro to Proofs/main.tex b/Advanced/Intro to Proofs/main.tex index 126d59b..8b3cf1e 100755 --- a/Advanced/Intro to Proofs/main.tex +++ b/Advanced/Intro to Proofs/main.tex @@ -220,10 +220,10 @@ Show that for any two functions $g: Y \to W$ and $h: Y \to W$, if $g \circ f = h \circ f \implies g = h$. - \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. - \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. \end{itemize}