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\author{Math 300 -- Spring 2019 (Hachtman)}
\title{Assignment 4: Equivalence Relations}
\date{Due Monday, March 11}

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\maketitle
For each of the following relations on the given sets, determine whether it is an equivalence relation, and prove your answer.
\begin{enumerate}
  \item The set of people: $x \mathbin{B} y$ iff $x$ and $y$ have the same birthday.
  
  \item The set of people: $x \mathbin{C} y$ iff $x$ and $y$ have citizenship in the same country.

  \item $\mathbb{R}$: $x \mathbin{R} y$ iff $x-y$ is a rational number.
  
  \item $\mathbb{R}^3$: $\mathbf{u} \mathbin{S} \mathbf{v}$ iff $\mathbf{u} \cdot \mathbf{v} = 0$.
\end{enumerate}

Write up your solutions in {\LaTeX} and submit them by email as usual.
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