To tackle this question, you need to identify the set of even integers greater than 4.
1. Understanding Even Integers Greater Than 4:
- An integer is even if it is divisible by 2.
- We are considering integers greater than 4. This includes numbers like 6, 8, 10, and so on.
2. Evaluating the Options:
Option a: [tex]\( \{6, 8, 10\} \)[/tex]
- This includes the numbers 6, 8, and 10. While these numbers fit the criteria, the set does not include all even integers greater than 4. It stops at 10.
Option b: [tex]\( \{5, 6, 7, \ldots\} \)[/tex]
- This set starts at 5, which is not an even number, and it includes all subsequent integers. It does contain even integers greater than 4, but it also contains odd integers and integers equal to or less than 4 (e.g., 5).
Option c: [tex]\( \{6, 8, 10, \ldots\} \)[/tex]
- This set starts at 6 and includes all even numbers that follow (8, 10, and so on). It correctly represents the set of even integers greater than 4, as it includes all subsequent even integers.
Option d: [tex]\( \{\ldots, -2, 0, 2\} \)[/tex]
- This set includes all even integers, both positive and negative, but it does not focus on those greater than 4. It includes negative numbers and zero, which do not meet the criteria.
Based on these evaluations, option c: [tex]\( \{6, 8, 10, \ldots\} \)[/tex] is the correct set representing even integers greater than 4.
