To find the inverse of a relation, we switch the $x$- and $y$-coordinates in each ordered pair.

Given relation: $\{ (3, 5), (-7, -1), (-5, 9), (5, -5) \}$

Switching the coordinates for each pair:

1. $(3, 5) \rightarrow (5, 3)$
2. $(-7, -1) \rightarrow (-1, -7)$
3. $(-5, 9) \rightarrow (9, -5)$
4. $(5, -5) \rightarrow (-5, 5)$

So, the inverse relation is: $\{ (5, 3), (-1, -7), (9, -5), (-5, 5) \}$

Let me know if you'd like further details or have any questions!

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Related Questions:

1. What is the general process for finding the inverse of a function?
2. How can you verify if two relations are inverses of each other?
3. Is the inverse of a function always a function? Explain.
4. What is the graphical interpretation of finding an inverse?
5. How does finding the inverse differ between relations and functions?

Tip: For an ordered pair $(a, b)$, its inverse will always be $(b, a)$, simply swapping the $x$- and $y$-values.