What is the property that states that a set is closed under addition and multiplication?

The correct answer is B, which refers to the closure property. This property indicates that when you perform a specific operation, such as addition or multiplication, on elements within a particular set, the result will also be an element of that same set. For example, in the set of integers, if you add two integers together or multiply them, the result is always another integer, which demonstrates that the set of integers is closed under both addition and multiplication.

This property is essential in various branches of mathematics, as it helps define mathematical structures, such as groups and rings, where operations must yield results within the same set for those structures to be consistent and useful. Understanding the closure property helps students see how different mathematical elements interact and can inform further exploration into more complex algebraic concepts.