Which property indicates a set is closed under an operation?

The property that indicates a set is closed under an operation is known as the Closure Property. This property asserts that if you take any two elements from a set and apply a specified operation (such as addition or multiplication), the result will also be an element of that same set.

For example, consider the set of integers and the operation of addition. If you take any two integers, say 3 and 4, the sum (7) is also an integer, thus showing that the set of integers is closed under addition. In contrast, if a set is not closed under an operation, applying the operation to elements of the set could yield a result that is not in the set.

The other properties mentioned—Identity, Associative, and Commutative—serve different purposes in mathematical operations. The Identity Property refers to an element that, when combined with another element using an operation, does not change the other element. The Associative Property deals with how the grouping of elements in an operation can be changed without affecting the outcome. The Commutative Property focuses on the ability to switch the order of the elements in an operation without changing the result. While these properties are important in their own right, they do not specifically address the concept of closure