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\title{CSCI 301 - Assignment 5, Fall 2024}
\author{Your name here}
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\noindent
Modify the .tex source file for this document, adding your answers below each question.\\
This is an individual assignment. See the syllabus for the collaboration policy.\\

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\begin{enumerate}

    \item (10 points) Let the relation $R$ on $\mathbb{Z}$ be defined as $R = \{(x, y) : 3 \mid (x+2y)\}$.
        \begin{enumerate}
            \item (6 points) Prove that $R$ is an equivalence relation.
            \item (4 points) Define each of $R$'s equivalence classes using set-builder notation. 

        \end{enumerate}

    \item (10 points) Consider the function $\theta: \{0, 1\} \times \mathbb{N} \rightarrow \mathbb{Z}$, defined as $\theta(a, b) = a - 2ab + b$. 
        \begin{enumerate}
            \item (5 points) Prove or disprove that $\theta$ is surjective.
            \item (5 points) Prove or disprove that $\theta$ is injective.
        \end{enumerate}



\end{enumerate}

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