To determine the set of even integers greater than 4, we need to consider the properties of even numbers and the specified condition that they must be greater than 4.
Step-by-step solution:
1. Identify Even Numbers:
- Even numbers are integers divisible by 2 without remainder. Examples of even numbers are 2, 4, 6, 8, 10, etc.
2. Apply the Condition (Greater than 4):
- We need to list only those even integers which are greater than 4.
3. List the Appropriate Elements:
- Starting from the first even number greater than 4: the next even number after 4 is 6.
- Continuing from 6, the next even number is 8.
- After 8, the next even number is 10.
- This sequence continues indefinitely.
4. Form the Set:
- The set of even integers greater than 4 can be written as [tex]\(\{6, 8, 10, \ldots\}\)[/tex], where the ellipsis indicates that the pattern continues indefinitely.
Given the multiple choices:
- a. [tex]\((6, 8, 10)\)[/tex] — This is a finite list and not a set, and it does not include the continuing sequence of even numbers.
- b. [tex]\(\{5, 6, 7, \ldots\}\)[/tex] — This includes all integers greater than 4, not just the even ones.
- c. [tex]\(\{6, 8, 10, \ldots\}\)[/tex] — This lists the even integers greater than 4 accurately and implies the continuation of the sequence.
- d. [tex]\(\{\ldots, -2, 0, 2\}\)[/tex] — This includes even integers but also those less than or equal to 4, which does not meet the condition.
The appropriate and correct set is:
c. [tex]\(\{6, 8, 10, \ldots\}\)[/tex]
