Added a problem

Advanced/Intro to Proofs/main.tex

@@ -101,4 +101,26 @@
 	\end{itemize}
 
 
+	\vfill
+	\pagebreak
+
+
+	\problem{}
+	Let $f$ be a function from a set $X$ to a set $Y$. We say $f$ is \textit{injective} if $f(x) = f(y) \implies x = y$. \par
+	We say $f$ is \textit{surjective} if for all $y \in Y$ there exists an $x \in X$ so that $f(x) = y$. \par
+	Let $A, B, C$ be sets, and let $f: A \to B$, $g: B \to C$ be functions. Let $h = g \circ f$.
+
+	\vspace{2mm}
+	\begin{itemize}
+		\item Show that if $h$ is injective, $f$ must be injective and $g$ may not be injective.
+		\item Show that if $h$ is surjective, $g$ must be surjective and $f$ may not be surjective.
+	\end{itemize}
+
+	\vfill
+	\pagebreak
+
+	\problem{}
+	
+
+
 \end{document}