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\leftline{Mathematics 243 -- Algebraic Structures}
\leftline{Definitions Quiz 4 -- October 6, 2006}
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\leftline{Your Name: $\underline{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }$}
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A) (5) State the three properties that define {\it equivalence relations}.  

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B) (5) Let $R$ be the relation on ${\bf Z}$ defined by $xRy$
if (and only if) $| x - y | \le 2$.  Is $R$ an equivalence relation?
Justify your answer.  
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