The problem asks us to find the inverse of the given relation.

Original Relation:

$\{(14, 10), (19, 10), (13, -3)\}$

Finding the Inverse:

The inverse of a relation is obtained by swapping the $x$- and $y$-coordinates in each ordered pair. Here's the result:

1. Swap $14$ and $10$: $(10, 14)$
2. Swap $19$ and $10$: $(10, 19)$
3. Swap $13$ and $-3$: $(-3, 13)$

Inverse Relation:

$\{(10, 14), (10, 19), (-3, 13)\}$

Let me know if you would like a deeper explanation or examples!

Related Questions:

1. What are the characteristics of a function's inverse in terms of ordered pairs?
2. Can a relation and its inverse both be functions? Explain with an example.
3. How do you determine whether an inverse relation is also a function?
4. How is the inverse of a relation represented graphically?
5. What is the difference between the inverse of a function and the inverse of a relation?

Tip: If the relation involves repeated $y$-values, the inverse might not be a function. Always verify by checking if any $x$-values repeat in the inverse.