Final answer:
The set of elements that are counting numbers and multiples of 4 consists of all positive integers that can be divided by 4 without a remainder, such as 4, 8, 12, 16, and so on. This set is infinite, as you can keep adding 4 to get the next multiple.
Step-by-step explanation:
The student asked to list the elements in the set x is a counting number multiple of 4. To answer this, we need to identify all positive integers (counting numbers) that can be divided by 4 without leaving any remainder. Counting numbers are the numbers we use to count; they start from 1 and go up indefinitely (1, 2, 3, ...). A multiple of 4 means any number that can be expressed as 4 times another counting number.
Examples of the first few multiples of 4 are 4, 8, 12, 16, and so on. The pattern is that each multiple is 4 units greater than the previous multiple. Therefore, the elements in the set requested by the student are all the counting numbers that fit this pattern. This set is infinite, as you can always find a higher counting number that is a multiple of 4 by simply adding 4 to the previous multiple.
To illustrate this, we could start with the first counting number multiple of 4, which is 4 itself, and then add 4 to get the next element, which is 8, and continue this pattern indefinitely.