To find the inverse of the given relation [tex]\(\{(4, 2), (6, 7), (8, 9), (5, -5)\}\)[/tex], you should follow these steps:
1. Understand the concept of the inverse of a relation: The inverse of a relation [tex]\(\{(a, b)\}\)[/tex] is obtained by swapping each pair to [tex]\(\{(b, a)\}\)[/tex].
2. Apply this concept to each pair in the given relation:
- The pair [tex]\((4, 2)\)[/tex] becomes [tex]\((2, 4)\)[/tex].
- The pair [tex]\((6, 7)\)[/tex] becomes [tex]\((7, 6)\)[/tex].
- The pair [tex]\((8, 9)\)[/tex] becomes [tex]\((9, 8)\)[/tex].
- The pair [tex]\((5, -5)\)[/tex] becomes [tex]\((-5, 5)\)[/tex].
3. Compile these new pairs to form the inverse relation:
- [tex]\((2, 4)\)[/tex]
- [tex]\((7, 6)\)[/tex]
- [tex]\((9, 8)\)[/tex]
- [tex]\((-5, 5)\)[/tex]
4. State the inverse relation: Therefore, the inverse relation [tex]\(\{(2, 4), (7, 6), (9, 8), (-5, 5)\}\)[/tex] is the answer.
In conclusion, the inverse of the relation [tex]\(\{(4, 2), (6, 7), (8, 9), (5, -5)\}\)[/tex] is:
[tex]\[
\boxed{\{(2, 4), (7, 6), (9, 8), (-5, 5)\}}
\][/tex]
