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\centerline{MATH 243 -- Mathematical Structures}
\centerline{Quiz 7 -- November 10, 2017}
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\noindent
Your Name: $\underline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}$
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\noindent
{\it Directions}
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Do all work and answer all questions on this sheet. (Use the back if you need more space.)  There are 30 possible points, 
distributed as indicated.    
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\begin{enumerate}
\item[A)]  (15)  Let 
$$f : \{ {\rm triangles\ in\ } \mathbb{R}^2\} \to (\mathbb{R}^+)^3$$ 
be the mapping that sends a triangle in the coordinate plane with vertices 
labeled as in $\Delta ABC$ to the ordered triple of positive numbers
given by the lengths of its sides, in the order $(AB,AC,BC)$.  For 
instance, if $T$ is the triangle with vertices $A = (0,0),B = (3,0), C = (0,4)$, then 
$f(T) = (3,4,5)$.  Does $f$ \emph{have an inverse mapping}? Why or why not? 
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\item[B)]  (15)  Let $R \subset A \times A$ be a relation.  What does it mean to say that
$R$ is an \emph{equivalence relation}?
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