added lab 1 problems on sequences

labs/lab1.tex

@@ -82,6 +82,48 @@ \section*{Warm up}
 No.
 \end{solution}
 
+\section*{Sequences}
+\question
+Give a function definition corresponding to each of the following sequences. Include the domain and codomain in your definition.
+
+\begin{parts}
+\part $(2,4,3,5)$
+\begin{solution}
+$f: \{0,1,2,3\} \to \{2,3,4,5\}$ where $f = \{(0,2),(1,4),(2,3),(3,5)\}$\\
+
+or\\
+
+$f: \{0,1,2,3\} \to \{2,3,4,5\}$ where $f(n) = n + 1 + ((n + 1) \mod 3) $ 
+\end{solution}
+
+\part $(a,d,c,b)$
+\begin{solution}
+$f: \{0,1,2,3\} \to \{a,d,c,b\}$ where $f = \{(0,a),(1,d),(2,c),(3,b)\}$
+\end{solution}
+
+\part $(1,3,5,7,9...)$
+\begin{solution}
+$f: \N \to O$ where $O$ is the set of odd natural numbers. $f(n) = 2n+1$ 
+\end{solution}
+
+\part $(1,4,9,16,25...)$
+\begin{solution}
+$f: \N \to S$ where $S$ is the set of perfect squares. $f(n) = (n+1)^2$ 
+\end{solution}
+
+\part $(0,1,-1,2,-2,...)$
+\begin{solution}
+$f: \N \to \Z$ where 
+$f(n) = \begin{cases}
+-\frac{n}{2} & \text{ if n is even}\\
+\frac{n+1}{2} & \text{ if n is odd}\\
+\end{cases} $
+\end{solution}
+
+\end{parts}
+
+
+
 \newpage
 \section*{Sets}
 \question