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\leftline{Mathematics 243 -- Algebraic Structures}
\leftline{Definitions Quiz 3 -- September 22, 2006}
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\leftline{Your Name: $\underline{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }$}
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A) (5) Let $f: A \to B$ be a mapping, and let $T \subseteq B$.  What
is the definition of the inverse image $f^{-1}(T)$? 
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B) (5) Let $f : {\bf Z} \to {\bf Z}$ be defined by 
$$f(x) = \cases{ 2x & if $x$ is odd\cr
                 x-1 & if $x$ is even\cr}$$
Is $f$ a permutation of ${\bf Z}$?  Justify your assertion.
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