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\leftline{Mathematics 243 -- Algebraic Structures}
\leftline{Definitions Quiz 2 -- September 15, 2006}
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\leftline{Your Name: $\underline{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }$}
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A) (5) Let $*$ be a binary operation on a set $A$.  What does it
mean to say that $*$ is {\it associative}.
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B) (5) Let $*$ be the binary operation on ${\bf Z}$ defined by 
$x * y = x + y - 7$.  Is there an identity element for $*$? 
If there is, say what it is and why it works; if not say why not. 
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