Explanation:

The set of natural numbers, denoted as N, is defined as the set of positive integers starting from 1 and going infinitely. It can be represented as {1, 2, 3, 4, ...}.

Upper Bound:
An upper bound is a number that is greater than or equal to all the elements of a set. In the case of the set of natural numbers, there is no number that is greater than or equal to all the elements since the set extends infinitely. For example, if we take any number N, there will always be a natural number greater than N. Therefore, the set of natural numbers does not have an upper bound.

Lower Bound:
A lower bound is a number that is less than or equal to all the elements of a set. In the case of the set of natural numbers, the number 1 is less than or equal to all the elements since the set starts from 1. Hence, 1 is a lower bound for the set of natural numbers. Therefore, the set of natural numbers has a lower bound.

Maximal Element:
A maximal element is an element in a set that is not smaller than any other element in the set. In the case of the set of natural numbers, there is no maximal element. Every natural number has a successor, meaning that there is always a larger natural number. For example, if we take any natural number N, N+1 will always be a larger natural number. Therefore, the set of natural numbers does not have a maximal element.

Conclusion:
In summary, the set of natural numbers has a lower bound (1), but it does not have an upper bound or a maximal element.