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

C:\Users\Adaji Adaji\Desktop\Photo0393.jpg

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
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