Final answer:
The set {4, 8, 12, 16,...} is infinite because it continues indefinitely following a pattern, where each number increases by 4 and there is no final element to the set.The correct option is: C. The set is finite because the number of elements in the set is a whole number.
Step-by-step explanation:
To determine whether the set {4, 8, 12, 16,...} is finite or infinite, we need to see if there is an end to the numbers listed or if they continue indefinitely. Since the set includes an ellipsis (...), this implies that the numbers continue following the same pattern without end. Each number in the set increases by 4, which indicates this is a sequence of multiples of 4. There is no final number in the pattern; thus, it can be concluded that the numbers will continue to increase by 4 indefinitely.
The correct answer to the question is B. The set is infinite because the elements of the set continue indefinitely, and there is no last number that we can point to as the final element of the set. The other options are incorrect because:
- Option A mistakenly implies that finiteness might be related to whether the number of elements is a whole number, which is not relevant to the concept of finite and infinite sets.
- Option C is incorrect because the set does not have a finite number of elements; it goes on forever.
- Option D is incorrect as it states there are no elements in the set, which is clearly not the case.The correct option is: C. The set is finite because the number of elements in the set is a whole number.