To solve the given problem, we need to identify the correct subset of integers that satisfy the condition [tex]\( y \geq 5 \)[/tex].
### Step-by-Step Solution:
1. Understand the Condition:
- We are looking for a set that includes all integers that are greater than or equal to 5.
2. Analyze Each Choice:
- Choice 1: [tex]\(\{5, 6, 7, 8, 9, \ldots\}\)[/tex]
- This set begins at 5 and includes all integers greater than or equal to 5. Therefore, it matches the condition [tex]\( y \geq 5 \)[/tex].
- Choice 2: [tex]\(\{6, 7, 8, 9, \ldots\}\)[/tex]
- This set begins at 6 and includes all integers greater than or equal to 6. Since it does not include 5, it does not satisfy the condition [tex]\( y \geq 5 \)[/tex].
- Choice 3: [tex]\(\{\ldots, 2, 3, 4, 5\}\)[/tex]
- This set includes integers that are less than or equal to 5 but does not include any integers greater than 5. Therefore, it does not match the condition [tex]\( y \geq 5 \)[/tex].
- Choice 4: [tex]\(\{-5, -4, -3, -2, \ldots\}\)[/tex]
- This set only includes negative integers. Hence, it does not satisfy the condition [tex]\( y \geq 5 \)[/tex].
3. Correct Choice:
- The correct choice is Choice 1: [tex]\(\{5, 6, 7, 8, 9, \ldots\}\)[/tex], as it includes all integers starting from 5 and extending to positive infinity. This set matches the condition [tex]\( y \geq 5 \)[/tex].
Thus, the correct elements in the set for [tex]\(\{y: y \text{ is an integer and } y \geq 5\}\)[/tex] are:
[tex]\[
\{5, 6, 7, 8, 9, \ldots\}
\][/tex]
Therefore, the correct answer is the first option.
