Download introduction to set

MATH 7
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INTRODUCTION TO
What
you will learned;
SET
 Basic concepts of sets.
 Kind of sets and Cardinality of
sets.
 Operation on sets
What is SETS?
A SET is a collection of well-defined
distinct objects or things.
Distinct means that elements should not be
repeated.
Elements the objects or things in the collection.
Normally, sets are denoted by CAPITAL
LETTERS.
EXAMPLE
A = {1, 2, 3, 4, 5 }
C = { l, o, v, e }
B = {1, 3, 5, …}
D = { c, a, r, e }
F = {x │ x ( this is read as set of x such that x) is a
positive number less than 6}
G = {y│ y is a letter from the alphabet}
H = {d │d is a number greater than 8}
There are two ways of describing a set.
 Listing/Roster method, in this form, we
enumerate or list all the element.
A variation of the simple roster method
uses the ELLIPSIS ( … ) when the pattern is
obvious and the set is large.
{1, 3, 5, 7, … , 9007} is the set of odd counting numbers less
than or equal to 9007.
{1, 2, 3, … } is the set of all counting numbers.
Listing/Roster method
Examples
1) A is a set of whole numbers less than 6.
A = { 0,1,2,3,4,5}
2) C is the set of letters in the
word excellent.
C = { e, x, c, l, n, t }
There are two ways of describing a set.
 Set-builder form ( Rule method) in
this method , we specify the rule or
property or statement.
Note: A = { x | x has a property of p}
This is read as A is the set of
elements x such that( | ) x has a
property p.
Set-builder form ( Rule method)
Example : A = { 2,4,6,8,10,12}
Solution :
In set A all the elements are even natural number
up to 12.So this is the rule for the set A
So set builder notation will be
A = { x | x is an even natural number, x ≤ 12}
 Set-builder form ( Rule method)
Example : K = { 10,11,12,13}
Solution :
In set K all the elements are numbers between 9
to 14 .So this is the rule for the set K
So set builder notation will be
K = { c │c are numbers between 9 to 14 }
How can you express the following in rule form
1. I = { 7, 8, 9, 10, 11, 12, 13, 14 }
I = {a | a are positive whole numbers
from 7 to 14}
How can you express the following in rule form
2. J = { m, a, t, h}
J = {b | b are letters of the word
math}
How can you express the following in rule form
3. L = {45, 46, 47, …}
L = {d | d are positive whole
numbers greater than 44}
How can you express the following in rule form
4. M = { 2, 1, 0, -1 ... }
M = {e | e are integer numbers
less than 3}
Practice Time
How can you express the following in rule form
into the roster method.
Rule Form
Roster Method
A ={x I x is an even number less
than 12 }
A = { 0, 2, 4, 6, 8,10}
F = { x I x is a vowel }
F = {a, e, i, o, u }
K = { x I x is an odd number greater
than 10 }
K = {11, 13, 15, 17,...}