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\leftline{Mathematics 243 -- Algebraic Structures}
\leftline{Definitions Quiz 8 -- November 16, 2012}
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\leftline{Your Name: $\underline{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }$}
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A) (5) Define:  $G$ is a {\it group} under the operation $*$.   

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B) (5)  Let $f : {\bf Z} \to {\bf Z}_4$ be the mapping that sends each integer
$x$ to its congruence class $[x]$ mod $4$.  Give a description of the set $f^{-1}(\{[0],[3]\})$.

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