What does it mean for a set to be "closed"?

Question

A. Members of a closed set cannot be added, subtracted, multiplied or divided.
B. An expression belonging to a closed set cannot be used to create an expression.
C. An operation performed on members of that set will result in a member of the same set.
D. The set has a finite number of members, as opposed to being infinitely large.

Answer 1

The correct answer is:

C. An operation performed on members of that set will result in a member of the same set.

In mathematics, a set is said to be "closed" under a certain operation (like addition, multiplication, etc.) if performing that operation on members of the set always produces a result that is also a member of the set. For example, the set of even integers is closed under addition, since the sum of any two even integers is also an even integer.