Question
What does it mean for a set to be "closed"?(1 point)
Responses
Members of a closed set cannot be added, subtracted, multiplied, or divided.
Members of a closed set cannot be added, subtracted, multiplied, or divided.
An operation performed on members of that set will result in a member of the same set.
An operation performed on members of that set will result in a member of the same set.
The set has a finite number of members, as opposed to being infinitely large.
The set has a finite number of members, as opposed to being infinitely large.
An expression belonging to a closed set cannot be used to create an expression that is not of that set.
Responses
Members of a closed set cannot be added, subtracted, multiplied, or divided.
Members of a closed set cannot be added, subtracted, multiplied, or divided.
An operation performed on members of that set will result in a member of the same set.
An operation performed on members of that set will result in a member of the same set.
The set has a finite number of members, as opposed to being infinitely large.
The set has a finite number of members, as opposed to being infinitely large.
An expression belonging to a closed set cannot be used to create an expression that is not of that set.
Answers
GPT-4o mini
The correct response is:
**An operation performed on members of that set will result in a member of the same set.**
In the context of mathematics, a set is considered "closed" under a certain operation if applying that operation to members of the set always produces a member that is also in the same set. For example, the set of even integers is closed under addition, because the sum of any two even integers is also an even integer.
**An operation performed on members of that set will result in a member of the same set.**
In the context of mathematics, a set is considered "closed" under a certain operation if applying that operation to members of the set always produces a member that is also in the same set. For example, the set of even integers is closed under addition, because the sum of any two even integers is also an even integer.