A binary operation is a mathematical operation that combines two elements from a set to produce another element from the same set. Common examples include addition, subtraction, multiplication, and division. In this context, the two elements are often referred to as operands, and the result is called the output. For instance, in the set of integers, the operation of addition takes two integers and produces another integer. Binary operations can be classified based on their properties. For example, an operation is called commutative if changing the order of the operands does not change the result, such as in addition and multiplication. An operation is associative if the grouping of the operands does not affect the outcome, as seen in addition and multiplication as well.