Questions: Write the set using set-builder notation. 2,4,6,8,10,12,14,16 Choose the correct set. A. x x is an even natural number B. x x is an even natural number less than or equal to 16 C. x x is a natural number less than or equal to 16

Solution Steps

To express the given set in set-builder notation, we need to identify a pattern or rule that describes all the elements in the set. The set \(\{2, 4, 6, 8, 10, 12, 14, 16\}\) consists of even natural numbers starting from 2 and ending at 16. Therefore, the correct set-builder notation should describe even natural numbers that are less than or equal to 16.

The given set is \(\{2, 4, 6, 8, 10, 12, 14, 16\}\). This set consists of even natural numbers starting from \(2\) and ending at \(16\).

To express this set in set-builder notation, we need to find a condition that describes all the elements. The elements are even natural numbers that are less than or equal to \(16\). Thus, the correct set-builder notation is: \[ \{x \mid x \text{ is an even natural number less than or equal to } 16\} \]

Now, we will evaluate the provided options:

• A. \(\{x \mid x \text{ is an even natural number}\}\) - This includes all even natural numbers, not limited to \(16\).
• B. \(\{x \mid x \text{ is an even natural number less than or equal to } 16\}\) - This matches our identified condition.
• C. \(\{x \mid x \text{ is a natural number less than or equal to } 16\}\) - This includes all natural numbers up to \(16\), not just the even ones.

Final Answer