A set can also be defined by giving a rule that determines whether an element is a member or not. For example, the expression

B = {x: x is a natural number between 10 and 20}

means that x is the collection of all natural numbers greater than 10 and less than 20. The set B above equivalently can be written as

B = {x| x is a natural number between 10 and 20}

or

B = {11, 12, ..., 19}.

Obviously, 15 ? B, 10 ? B, 25 ? B. The notations {x: …} and {x| …} are called implicit representations of sets.

As also understood from the information given, “A = {x| x is a natural number between 30 and 40" and “ A = {x: x is a natural number between 30 and 40}” are the implicit representations of the set  A= {31, 32, 33,…39}, so the correct answer is A.

The expression “A = {x| x is a natural number}” is not well-defined, so it is not a set.

The expression “A is its own subset.” in the option IV explains the notion of set, but it is not the implicit representation of the set A.