To determine if two relations are inverses of each other, we need to confirm whether each pair of points \((x_1, y_1)\) from one table corresponds to the pair \((y_1, x_1)\) from the other table. This means if \((x, y)\) exists in one table, then \((y, x)\) should exist in the second table.
Let's analyze the given tables:
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Table 1:
- Points: \((-2, 2), (-1, 1), (0, 0), (1, -2), (2, -1)\)
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Table 2:
- Points: \((-2, 0), (-1, 2), (0, 1), (1, -2), (2, -1)\)
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Table 3:
- Points: \((-2, 1), (-1, 2), (0, -2), (1, 0), (2, -1)\)
Now, let's check pairs between each table:
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Table 1 and Table 2:
- Table 1 has point \((-2, 2)\). Table 2 does not have point \((2, -2)\).
- Conclusion: Not inverses.
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Table 1 and Table 3:
- Table 1 has point \((-2, 2)\). Table 3 does not have point \((2, -2)\).
- Conclusion: Not inverses.
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Table 2 and Table 3:
- Table 2 has point \((-2, 0)\). Table 3 does not have point \((0, -2)\).
- Conclusion: Not inverses.
Since no pair of tables satisfies the conditions for being inverses of each other, none of the tables represent relations that are inverses.