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The Language of Set

The document discusses sets and their definitions, properties, and methods of description. A set is a well-defined collection of distinct objects. Sets can be described using either a roster method, which lists the elements between braces, or a rule method using set-builder notation to define a property the elements must have to be included in the set. Examples are provided to illustrate both methods.

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Denise Briones
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198 views12 pages

The Language of Set

The document discusses sets and their definitions, properties, and methods of description. A set is a well-defined collection of distinct objects. Sets can be described using either a roster method, which lists the elements between braces, or a rule method using set-builder notation to define a property the elements must have to be included in the set. Examples are provided to illustrate both methods.

Uploaded by

Denise Briones
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PPTX, PDF, TXT or read online on Scribd
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Let's learn

about SETS
SET
DEFINITIO
N – a well-defined
collection of
distinct objects.
Example # 1:​ Example # 2:​
A collection of enrolled
students in an English A collection of all the days
class is a set. of the week is a set.
A collection of
five best
basketball
players of all
time

NOT a set
 Sets are denoted by capital letters
(e.g. A, D, C,…). The objects of a
set are separated by comma and
are enclosed by braces.
 These objects are called
the elements or members of the
 Facts about set.
Sets  If A is a set, the notation x ∈ A
means that x is an element of A.
(x belongs to A)
 The notation x ∉ A means that x
is not an element of A.
  A set contains the months of the year
beginning with the letter J
M = {January, June, July}

How do we  January ∈ M
write a set and August ∉ M 
its elements?   A set contains the whole numbers less
than 5
L= {0, 1, 2, 3, 4}
 3 ∈ L
10 ∉ L 
1. ROSTER METHOD or
Listing Method
     - list all the elements of the
set enclosed with braces
Ways of       
describing sets Examples:​

 M = {January, June, July}​

L= {0, 1, 2, 3, 4}
For sets with more elements,
show the first few entries to
display a pattern, and use an
Ways of ellipsis (…) to indicate “and so
describing on.”
sets
Example:
The set of the first 50
positive integers. ​
{1,2,3,…,50} 
2. RULE METHOD or SET
BUILDER NOTATION
 Let S denote a set and let P(x) be
a property that elements of S
may or may not satisfy. We
may define a new set to be the
Ways of set of all elements x in S such
describing sets that P(x) is true.
    
 {x ∈ S | P(x)}     

The set of all such that


Example # 1:​
a. The collection of all the months
of a year beginning with the letter
J
b. The collection of whole
    
numbers less than 5

EXAMPLES Answers:

a. {x|x is a month of the year


which begins with letter J}

b. {y|y is a whole number less


than 5}
a. The collection of all the months
of a year beginning with the letter
J
b. The collection of whole
numbers less than 5
    
ROSTER METHOD:​
Roster Method
and Rule  M = {January, June, July}​
Method L = {0, 1, 2, 3, 4}
RULE METHOD:​
a. {x|x is a month of the
year which begins with
letter J}​
b. {y|y is a whole number less
than 5}
Write the following sets in
Rule Method and Roster
Method:​
    
1. The set of all even
numbers less than 12
TRY THIS!
2. The set of all letters in
the word
"MATHEMATICS" 
(Hint: repetition is not important in
sets.)

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