Final answer:
The equivalent statement to 'If all elements of an infinite set A are natural numbers then there exists the smallest element in this set' is 'If there is the smallest element in this set, then not all elements of a set A are natural numbers', which is reflected in option C.
Step-by-step explanation:
If all elements of an infinite set A are natural numbers, then there necessarily exists the smallest element in this set. This statement is based on the well-defined properties of natural numbers, which start from 1 and continue indefinitely in a discrete manner. The statement we are examining is logically equivalent to: "If there exists the smallest element in this set, then not all elements of a set A are natural numbers." In other words, acknowledging the existence of a minimum means that the set can't be composed entirely of items that are not natural numbers, as not natural numbers include irrationals, negatives, and complex numbers, which do not have a clear smallest element due to their defined properties.
Option C appears to best reflect this notion: If there is the smallest element in this set, then not all elements of a set A are natural numbers. This choice mirrors the logical structure of the original statement by using the presence of a minimum to refute the situation where no elements are natural numbers.