To solve the problem shown in the image, we need to find the inverse of the relation $\{(2, 5), (0, 6), (-3, 4)\}$.

Step-by-Step Solution:

1. Definition of an Inverse Relation: The inverse of a relation is found by swapping the first and second elements in each ordered pair.

2. Apply the Inversion:

   • For the pair $(2, 5)$, its inverse is $(5, 2)$.
   • For the pair $(0, 6)$, its inverse is $(6, 0)$.
   • For the pair $(-3, 4)$, its inverse is $(4, -3)$.

   So, the inverse relation is: $\{(5, 2), (6, 0), (4, -3)\}$

Answer:

The correct answer is the first option: $\{(5, 2), (6, 0), (4, -3)\}$.

Would you like further clarification on any steps?

Here are five related questions:

1. What is the inverse of the set $\{(1, 3), (4, 2)\}$?
2. How do you determine if a relation has an inverse?
3. Can all functions have an inverse? Why or why not?
4. What is the difference between a function and its inverse in graphical terms?
5. How do you find the inverse of a function algebraically?

Tip: The inverse of a relation may not always be a function unless the original relation passes the horizontal line test (ensuring it’s one-to-one).