Questions: Which table represents the same relation as the set (-6,4),(-4,0),(-3,2),(-1,2) ? Table 1: x y -6 -3 4 2 -4 -1 0 2 Table 2: x y -6 4 -4 0 -3 2 -1 2 Table 3: x y 6 4 4 0 3 2 1 2

Solution Steps

The given relation is the set \(\{(-6,4),(-4,0),(-3,2),(-1,2)\}\). This means the pairs \((x, y)\) are \((-6, 4)\), \((-4, 0)\), \((-3, 2)\), and \((-1, 2)\).

The first table is: \[ \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline -6 & -3 \\ \hline 4 & 2 \\ \hline -4 & -1 \\ \hline 0 & 2 \\ \hline \end{tabular} \] The pairs in this table are \((-6, -3)\), \((4, 2)\), \((-4, -1)\), and \((0, 2)\). None of these pairs match the given relation.

The second table is: \[ \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline -6 & 4 \\ \hline -4 & 0 \\ \hline -3 & 2 \\ \hline -1 & 2 \\ \hline \end{tabular} \] The pairs in this table are \((-6, 4)\), \((-4, 0)\), \((-3, 2)\), and \((-1, 2)\). These pairs exactly match the given relation.

Final Answer