SS1 First Term Further Mathematics Lesson Note – Sets

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WEEK FOUR

SETS

CONTENTS:

1. Definition of set
2. Set notation methods
3. Types of sets: Null set, Singleton set, Finite and infinite set, Subsets, Universal set and Power set.
4. Law of algebra of sets

SUB TOPIC: DEFINITION OF SET

A set is a collection of distinct objects, things, objects or numbers.

Examples includes:

1. A collection of books in public or private library
2. A collection of tools in a carpentry workshop
3. Letters of the alphabet
4. The collection of all positive numbers

Basically we can conclude that any clearly defined collection of things, objects or numbers constitutes a set.

When the number of elements in a given set is countable, the set is called a FINITE SET. E.g whole numbers lying between 1 and 10, members of a football team, etc. but if the number of elements in a set is not finite/countable, then the set is called an INFINITE SET. E.g real numbers, rational numbers, etc.

CLASS ACTIVITIES:

1. Define set
2. List five (5) examples of sets
3. Differentiate between a finite set and an infinite set with five (5) examples each.

SUB TOPIC: SET NOTATION METHODS

Each member of a set is called an element of the set. Capital letters  will be used to denote sets while small letters  will be used to denote the elements of a set.

When an element  belongs to a set , we write and say that  is a member or element of  If is not a member or element of  we write  and say that does not belong to .

Example:

If  is the set of all prime numbers and  then . If , then .

A set is completely specified in the following ways:

1. By lising all the members of the set;
2. By describing the elements of the sets;
3. By enclosing the members or elements in curly bracket or braces: {} or .

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