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Write the set by listing the elements: \{n is an even integer greater than 4\}. Choose the appropriate set from the possibilities listed below.

A. [tex]$(6,8,10)$[/tex]
B. [tex]$\{5,6,7, \ldots\}$[/tex]
C. [tex]$\{6,8,10, \ldots\}$[/tex]
D. [tex]$\{\ldots,-2,0,2\}$[/tex]


Sagot :

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]
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