To determine the domain of a given relation, we need to examine the set of first elements in each ordered pair within the relation.
The given relation is:
[tex]\[
\{(1, 2), (4, -5), (-3, 1), (1, 3)\}
\][/tex]
1. Look at each ordered pair in the relation:
- For [tex]\((1, 2)\)[/tex], the first element is [tex]\(1\)[/tex].
- For [tex]\((4, -5)\)[/tex], the first element is [tex]\(4\)[/tex].
- For [tex]\((-3, 1)\)[/tex], the first element is [tex]\(-3\)[/tex].
- For [tex]\((1, 3)\)[/tex], the first element is [tex]\(1\)[/tex].
2. Collect all unique first elements from these pairs:
[tex]\[
\{1, 4, -3\}
\][/tex]
Hence, the domain of the given relation [tex]\(\{(1, 2), (4, -5), (-3, 1), (1, 3)\}\)[/tex] is [tex]\(\{1, 4, -3\}\)[/tex].
We now compare this with the given options:
- Option A: [tex]\(\{-5, -3, 1, 2, 3, 4\}\)[/tex]
- Option B: [tex]\(\{1, 3, 4\}\)[/tex]
- Option C: \{-3, 1, 4\}\)
- Option D: [tex]\(\{-5, 1, 2, 3\}\)[/tex]
The correct domain from these options is:
[tex]\[
C: \{-3, 1, 4\}
\][/tex]
Therefore, the domain of the relation is the set [tex]\(\{-3, 1, 4\}\)[/tex], which corresponds to Option C.
