set miss.namthip meemag wattanothaipayap school. definition of set set is a collection of objects,...

SETMiss.Namthip Meemag

Wattanothaipayap School

Definition of Set

• Set is a collection of objects, things or symbols.

• There is no precise definition for the term “Set”.

• For example - A set of coins - A set of students in Science Classrooms

The members or elements of Set• The individual objects in a set are call the members or elements.

• There are two ways to be clearly defined a set

- Listing the elements

- Describing the elements

Listing the elements

B a,b,c,d

A 2,4,6,8,10

The capital letter to denote a set.The small letter to denote member of a set.

Describing the elements

B x|xisanevennumberlessthan12

A x|xisacitizenofThailand

C x|xisariverinChaingmai

“A is the set of elements x such

that x is a citizen of Thailand”

Example 1

• List all the elements in each of the following sets.

(a) The set of vowels in the English alphabet.

(b) The set of positive odd numbers less than 10.

(c) The set of letters used in the “WOOD”

Solution 1

(a) a,e,i,o,u

(b) 1,3,5,7,9

(C) W,O,D

Example 2

(a) A Monday,Tuesday,Wednesday,Thursday,Friday,Saturday,Sunday

(b) B 1,2,3,4,5

Describe the following set in words

Solution 2

(a)A is the set of days in the week

(b)B is the set of the first five natural numbers

B is the set of the countable numbers less than 6

Example 3

• State whether each of the following collection is a well-defined set (Give a reason for your)

(a) A set of a book well – liked by my classmates.

(b) A set of a handsome man in this class.

(c) A set of a Mathematics teacher in my class.

Null or Empty Set

A = { x | x is a positive integer less than 1 }

= { }A = We called that “Null set or Empty set”

Finite and Infinite Set

A = {1, 2, 3, 4, 5}B = { x | x is an integer} = { …, -2, -1, 0, 1, 2, …}

We called that A is a finite set and B is a Infinite set

Universal Set

•The set which contains all the other sets in a discussion is called the universal set

•We denoted its by the symbol “U”

Set Equality

A = { Beer, Big, Bank} B = { Big, Beer, Bank}

We say that A equal to B or A = B

C = {a, e, i, o} D = {a, e, i, o, u}

We say that C not equal to D or C D

Disjoint Sets and Complement of a set

Let U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

A = {0, 1, 2, 3, 4} B = {5, 6, 7, 8, 9}

We say that A and B are disjoint set

And B is the complement of A denoted by B =

A is the complement of B denoted by A =

AB

Example 4

If U = {2, 3, 5, 7, 10, 13, 17}, A = {2, 3, 5}

B = {10, 13, 17} and C = {7, 13}.

Find , , . And write down two pairs of disjoint sets.

A B C

Subsets

If each member of a set B is also a member of a

set A, then the set B is called a subset of the set A

We used the notation B A to denote that B is a

subset of ANote : We regard as a subset of any set

Subsets

Consider the set A = {a, b, c, d, e}

B = {a, c, d} C = {d, a, c}

Is C A?, Is C B?, Is B C?

So, if C B and B C, then C = B

Subsets

If A = {1, 2, 3} find any subsets of A.

How many subsets of A are there?.

Subsets of A are { }, {1}, {2}, {3}, {1, 2}, {1, 3},

{2, 3}, {1, 2, 3}

The number of subsets is 8

Power set

Consider that A = {1, 2, 3} subsets of A are

{ }, {1}, {2}, {3}, {1, 2}, {1, 3},{2, 3}, {1, 2, 3}

The set of all subsets is called Power set denoted

P(A) = {{ },{1},{2},{3},{1, 2},{1, 3},{2, 3},{1, 2, 3}}

Power set

Given that A = {x, y} , what’s P(A)?

P(A)= {{ }, {x}, {y}, {x, y}}

The number of subsets for set A is 2n(A)

The End

Miss.Namthip Meemag

Wattanothaipayap School