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COMPUTER SCIENCE 20, SPRING 2012 \\
DISCRETE MATHEMATICS FOR COMPUTER SCIENCE\\
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Class \#10 (Relations)
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\paragraph{Homework, due in hard copy Wednesday 2/15/2012 at 10:10am}
\paragraph{Please write your TF's name on your homework, and list the names of any students with whom you collaborated.}
\begin{enumerate}
\item Find a bijection between the set of all integers and the set of non-negative integers. That is, give a rule/formula assigning each integer to a non-negative integer and vice versa.
\item \begin{enumerate}
\item Show that if two finite sets $A$ and $B$ are the same size, and $r$ is a total injective function from $A$ to $B$, then $r$ is also surjective; i.e. $r$ is a bijection.
\item Give a counterexample showing that the conclusion of part (a) does not necessarily hold if $A$ and $B$ are two infinite sets that have the same cardinality.
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