BINARY OPERATIONS: BASIC CONCEPT OF BINARY OPERATIONS

FURTHER MATHEMATICS SSS1 FIRST TERM

WEEK 7

BINARY OPERATIONS: BASIC CONCEPT OF BINARY OPERATIONS

Contents

• Concept of binary operations,
• Closure property
• Commutative property
• Associative property and
• Distributive property.

Definition:

A binary operation is any rule of a combination of any two elements of a given non-empty set. The rule of combining two elements of a set may give rise to another element that may or may not belong to the set under consideration.

 It is usually denoted by symbols such as, *, Ө e.t.c.

                                                                                               

Properties:

A. Closure property: A non-empty set z is closed under a binary operation * if for all a, b € Z.

Example; A binary operation * is defined on the set S= {0,…