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Chapter 13 Binary Operations
Objectives
Show that there is an identity with respect to a binary operation.
Show that an element has an inverse with respect to a binary operation.
Recognize whether a binary operation is associative.
Show that a binary operation is commutative.
Binary operations generalize the concept of operations that you have encountered already, such as addition, subtraction, multiplication, and addition. More precisely formulated a binary operation is a function on a set that combines two elements of the set to form a third element of the set.
In this chapter, after formally defining binary operations, we consider four properties of the binary operations, that we have already encountered in special cases. These properties are:
Existence of an identity element,
Existence of inverses,
Associativity, and
Commutativity
Exactly theses properties are also the subjects of the sections in the chapter:
