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\begin{document}

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\noindent{\Large{\textsc{Intro to Abstract Mathematics\hfill Assignment 11.2  \\ Spring 2020 \hfill Due April 22}}}

\large

\vspace{1cm}


\begin{exercise}
Prove that $C = \{ (x,y) \in \R^2  \, | \, x - y \in \Z\}$ is an equivalence relation on $\R$.
\end{exercise}

\begin{exercise}
Prove that $P = \{ (\mathbf{v},\mathbf{w}) \in \R^2 \times \R^2 \, | \, \exists \lambda \in \R^{\times}(\mathbf{v} = \lambda \mathbf{w}) \}$ is an equivalence relation on $\R^2$.  Here $\R^{\times} = \R \setminus \{ 0 \}$.
\end{exercise}



\end{document}
