Math  /  Algebra

QuestionMy sweet Christine, tis best if we can improve our relations. Remember that relations may take many different forms and look different ways -- masks of a sort. Unfortunately only one of our famous Greek friends could translate their relation correctly every time. Who's right? R={(1,4),(2,5),(5,5),(2,3),(1,1)}R=\{(1,4),(-2,5),(5,5),(2,3),(-1,-1)\} \begin{tabular}{|c|c|c|c|c|} \hline Greek Mathematician & Domain \& Range & Table, Mapping Relation, or Graph & Is it a Function? & Inverse \\ \hline Aristotle x=10x=10 &  D: {2,1,1,2,5} R: {1,3,4,5}\begin{array}{l} \text { D: }\{-2,-1,1,2,5\} \\ \text { R: }\{-1,3,4,5\} \end{array} & \begin{tabular}{|c|c|} \hlinexx & yy \\ \hline 1 & 4 \\ \hline-2 & 5 \\ \hline 5 & 5 \\ \hline 2 & 3 \\ \hline-1 & -1 \\ \hline \end{tabular} & Yes & {(4,1),(2,5),(5,5),(3,2),(1,1)}\begin{array}{l} \{(4,1),(2,-5), \\ (5,5),(3,2), \\ (-1,-1)\} \end{array} \\ \hline Euclid e=5e=-5 & \begin{tabular}{l} D: {2,1,1,2,5}\{-2,-1,1,2,5\} \\ R:{1,3,4,5}R:\{-1,3,4,5\} \end{tabular} & & Yes & {(4,1),(5,2),(5,5),(3,2),(1,1)}\begin{array}{l} \{(4,1),(5,-2), \\ (5,5),(3,2), \\ (-1,-1)\} \end{array} \\ \hline Plato u=4u=-4 & D:{2,1,1,3,5}R:{1,2,4,5}\begin{array}{l} \mathrm{D}:\{-2,-1,1,3,5\} \\ \mathrm{R}:\{-1,2,4,5\} \end{array} & (12521)\left(\begin{array}{rl} 1 \\ -2 \\ 5 & \longrightarrow \\ 2 \\ -1 \end{array}\right) & Yes & {(4,1),(5,2),(5,5),(3,2),(1,1)}\begin{array}{l} \{(4,1),(5,-2), \\ (5,5),(3,2), \\ (-1,-1)\} \end{array} \\ \hline Ptolemy ω=0\omega=0 &  D: {2,1,1,2,5} R: {1,3,4,5}\begin{array}{l} \text { D: }\{-2,-1,1,2,5\} \\ \text { R: }\{-1,3,4,5\} \end{array} & & Yes & {(4,1),(5,2),(5,5),(3,2),(1,1)}\begin{array}{l} \{(4,1),(5,-2), \\ (5,5),(3,2), \\ (-1,-1)\} \end{array} \\ \hline Pythagoras k=20k=20 & D:{2,1,1,2,5}R:{1,3,4,5}\begin{array}{l} \mathrm{D}:\{-2,-1,1,2,5\} \\ \mathrm{R}:\{-1,3,4,5\} \end{array} & & No & {(4,1),(5,2),(5,5),(3,2),(1,1)}\begin{array}{l} \{(4,1),(5,-2), \\ (5,5),(3,2), \\ (-1,-1)\} \end{array} \\ \hline \end{tabular}

Studdy Solution
Now, compare each Greek mathematician's claims: - Aristotle: Correct domain and range, correct table, correct function status, incorrect inverse. - Euclid: Correct domain and range, correct function status, correct inverse. - Plato: Incorrect domain and range, incorrect table, incorrect inverse. - Ptolemy: Correct domain and range, correct function status, correct inverse. - Pythagoras: Correct domain and range, incorrect function status, correct inverse.
Euclid and Ptolemy have the correct descriptions. Since the problem asks for only one, we can choose either.
The Greek mathematician who is right is:
Euclid or Ptolemy \text{Euclid or Ptolemy}

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