- Identify each row of the table as an ordered pair \((x, y)\): \((10, 5)\), \((14, 2)\), and \((11, 19)\).
- Assemble these pairs into a set notation \(\{(10, 5), (14, 2), (11, 19)\}\).
- Compare the result with the given choices to find the matching option.
- The correct set is \(\boxed{\{(10, 5), (14, 2), (11, 19)\}}\).
Explanation
- Extracting the Ordered Pairs
The problem asks to represent a relation given in a table as a set of ordered pairs. A relation is a collection of ordered pairs where each pair \((x, y)\) consists of an input \(x\) and its corresponding output \(y\). Looking at the provided table:
| \(x\) | \(y\) |
| :--- | :--- |
| \(10\) | \(5\) |
| \(14\) | \(2\) |
| \(11\) | \(19\) |
We read the table row by row to extract the pairs. The first row gives us the pair \((10, 5)\), the second row gives us \((14, 2)\), and the third row gives us \((11, 19)\).
- Forming the Set of Ordered Pairs
Now that we have identified the individual ordered pairs, we collect them into a set notation. A set of ordered pairs is denoted by placing the pairs inside curly braces \(\{ \dots \}\). Combining our findings, the set of ordered pairs representing the relation is \(\{(10, 5), (14, 2), (11, 19)\}\). This matches the third option provided in the problem.
Examples
In data science and statistics, representing data as a set of ordered pairs is essential for visualization. For example, if you track the temperature (\(y\)) at different hours of the day (\(x\)), you get a set of points that can be plotted on a coordinate plane. This helps identify trends, such as whether the temperature rises or falls over time, and is the foundational step for creating graphs that represent real-world phenomena like weather patterns or stock market fluctuations.