Questions: Use the following roster notations to write in set builder notation, use x as the variable.
2,4,6,8,10,12,14,16,18,20,22,24,26
x x is an integer between 1 and 27
Transcript text: Use the following roster notations to write in set builder notation, use $x$ as the variable.
\[
\{2,4,6,8,10,12,14,16,18,20,22,24,26\}
\]
\{ $x$ | $x$ is an integer between 1 and 27 \}
Solution
Solution Steps
To convert the given roster notation to set builder notation, we need to identify the pattern in the set. The set contains even numbers starting from 2 and ending at 26. We can express this as a set of all even integers between 2 and 26 inclusive.
Step 1: Identify the Set
The given roster notation is \(\{2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26\}\). This set consists of even integers starting from 2 and ending at 26.
Step 2: Express in Set Builder Notation
To express this set in set builder notation, we can define it as:
\[
\{ x \in \mathbb{Z} \mid 2 \leq x \leq 26 \text{ and } x \text{ is even} \}
\]
This means \(x\) is an integer between 2 and 26, inclusive, and \(x\) must be even.
Step 3: Verify the Set
The set builder notation correctly represents the original set, as it includes all even integers from 2 to 26. The output confirms that the set is:
\[
\{2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26\}
\]
Final Answer
The set in set builder notation is:
\[
\boxed{\{ x \in \mathbb{Z} \mid 2 \leq x \leq 26 \text{ and } x \text{ is even} \}}
\]