Types of sets: Null set, Singleton set, Finite and infinite set, Subsets, Universal set and Power set.

WEEK FOUR

SS1 FURTHER MATHS FIRST TERM

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:[mediator_tech]

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 .

CLASS ACTIVITIES:

1. (a). What is an element of a set? (b). Write out another name for element of a set
2. What is the meaning of the following signs in set notations:
3. . (b).
4. If is the set of even numbers and , then is what to

SUB TOPIC: TYPES OF SET

1. Null or empty set: When a set contains no element or member is said to be null or empty set and denoted by .

Examples:

1. Human beings with tails}
2. {all prime members of SS1 class divisible by 4}
3. Singleton or unit set: A set which consist of only one element or member is called unit or singleton set.

Example: is a unit or singleton set because it contains only one element.

1. Finite set: When the number of elements in a given set is finite can be be listed or stated.

Example:

is finite.

The members of the set

1. Infinite set: If the number of element in a set is not finite or cannot be listed.

Example:

, since we can not list all the element in the set

1. Subset: if all the elements of the set are members of a set the set is a subset of We denote this by a set notation. Thus, means is a subset of
2. A proper subset of If the set is a subset of and there is at least one element in the set which is not in then the set is called a proper subset of or is superset of set . Thus means is a proper subset of Thus means is a superset of
3. Universal set: The set which contains all the possible elements under consideration. The universal set is denoted by .
4. Power set: The set of all subsets of a set The power set is usually denoted by

CLASS ACTIVITIES:

1. Mention the types of sets you know.
2. Explain with example a universal set.
3. What is a subset?
4. Explain the difference between a proper subset and superset.

SUB TOPIC: LAWS OF ALGEBRA OF SET

Consider the diagram below involving three sets

Commutative Laws

Associative Laws

Distributive Laws

Idempotent Laws

De Morgan’s Laws

Laws of Complementation

Additional Properties

Laws of Inclusion

PRACTICE EXERCISE:

Objective Test:

1. ………………is a collection of distinct objects, things or numbers
2. Set B. elements C. members D. universal E. notation
3. Each member of a set is called an……………..[mediator_tech]
4. Subset B. superset C. elements D. finite E. singleton
5. Which bracket is use in enclosing the elements of a set?
6. Big bracket B. small bracket C. open bracket D. curly bracket E. set bracket.
7. The sign of subset is………… A. B. C. D. E.
8. …………….set is a which contains all the possible elements under consideration?
9. Universal B. power C. finite D. singleton E. null

Essay Questions

{all the days in a week}; {all the days whose letters begin with T}

1. List all the elements of
2. List the members of
3. List the members of
4. What is ?
5. What is ?

KEY WORDS

• SETS
• COLLECTION
• ELEMENT
• MEMBER
• UNION
• INTERSECTION
• UNIVERSAL
• PRIME/COMPLEMENT
• VENN DIAGRAM
• SUBSET
• NULL SET
• POWER SET
• CARDINAL SET
• NOTATION
• OPERATIONS