What is the domain of the relation {(1, 3), (3, 2), (1, 4), (4, 5), (5, 2)}?
*
{5, 1, 3, 4}
{4, 2, 1, 3, 5}
{2, 4, 5, 3}
{1, 5, 1, 4, 3}

The domain of a relation consists of all the first elements (or x-values) from each ordered pair in the set. Given the relation \(\{(1, 3), (3, 2), (1, 4), (4, 5), (5, 2)\}\), let's identify the first elements of each pair:

- \( (1, 3) \) → 1
- \( (3, 2) \) → 3
- \( (1, 4) \) → 1
- \( (4, 5) \) → 4
- \( (5, 2) \) → 5

Now, collecting all these first elements, we have the set \(\{1, 3, 1, 4, 5\}\).

Since sets do not contain duplicate elements, we simplify this to \(\{1, 3, 4, 5\}\).

So, the correct answer is: **\(\{1, 3, 4, 5\}\)**, which matches the option \(\{1, 5, 1, 4, 3\}\) after reordering.

Would you like more details or have any questions? 

Here are 5 related questions:
1. What is the range of the relation \(\{(1, 3), (3, 2), (1, 4), (4, 5), (5, 2)\}\)?
2. How do you determine if a relation is a function?
3. What is the difference between a domain and a range?
4. Can a relation have repeated elements in its domain?
5. How do you represent a relation on a graph?

**Tip:** When analyzing relations, always check if there are duplicate elements in the domain or range, as this can help in determining if the relation is a function.

Learn how to determine the domain of a relation {(1, 3), (3, 2), (1, 4), (4, 5), (5, 2)} in set theory. Understand the concept of domain as the set of all first elements in the ordered pairs of a relation. Suitable for high school students studying set theory and relations.

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