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Name:___________ Teacher: WL Cheng Class : 4A

Lesson No.:6

Sekolah Menengah Seri Omega Date : 6//!"Time : ##.$! % #.4!

S&'(ect: Mathematics

Cha)ter:$

To)ic: Sets *#+

S&',to)ic:

Notes:,

$.#a De-ining Sets

a. Set refers to any collection orgroup of

objects.

b. Sets are usually specified in three ways.

(a) The description method Example

{odd numbers}

(b) The roster method In this method, the set is defined by listin the numbers.

Example

{!, ", #, $, %.}

(c) Using set-builder notation

This combines both the roster and description method.

Example

{ :x x is an odd positi&e number}

b. The objects in a set are called elements or

members of the set. They are said to belon

to the set.

d. Sets are usually denoted by capital letters

and the notation used for sets is braces, { }.

Example

'{, *, +, }

e. The definition of sets has to be clear and

precise so that the elements can be identified.

f. The same elements in a set need not be

repeated.

Example

- = {letters in the word belie&e/ }

{b,e,i,l,&}

ercise $.#a

# List the elements o- each o- the -ollo0ing sets. *a+0 1 2m&lti)les o- ##3 less than !5

*'+1 {-irst -ie letters o- the al)ha'et5

*c+2 2o0els in the 0or7 8CLASS95

.

*7+ 32x4 x is a -actor o- #5

*e+5 1 2names o- states in Malasia starting 0ith15

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De-ine the -ollo0ing sets &sing a statement or

a 0or7.

*a+ M12#3;5

*'+

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*e+62p4 $ p ;3pis a 0hole n&m'er5

6otes47a. The notation n(') denotes the number of elements in set A.

b.=hen a 9enn diaram represents the number

of elements in a set, no dot is placed to the

left of the number.

4 or each o- the -ollo0ing sets3

*a+ list the elements in the set3

*'+ the n&m'er o- elements in the set3*c+ 7ra0 a ?enn 7iagram to re)resent the

n&m'er o- elements in the set

*i+ > *-actors o- #B5

*ii+ S 1 2letters in the 0or7 ?:@9EA 5

*iii+ T 1 2ca)itals o- states in Malasia starting 0ith S5 .

*i+ E 1 2t0o 7igit n&m'ers less than # 0hose &nits 7igit is less than 5

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*+0 1 2)rime -actors o- !5

*i+B 1 2x4 $ x $! an7x is een5

6otes47

' set with no elements is called an empty set

or a null set. The symbol (phi) or empty

braces, { }, denotes an empty set. Therefore,

if set > is an empty set, then > { } or >

and n(>) C.

or each o- the -ollo0ing sets3

*a+ list the elements in the set3 *'+ state the n&m'er o- elements in the set3

*c+ state 0hether the set is an em)t set or

not &sing set notation.

*i+ A 1 2-actors o- 7iisi'le ' $5

*ii+- 1 2consonants in the 0or7

;3@@D;5

*iii+ C1 2x4x !,x is a negatie n&m'er5

6otes47a. Two sets are equal if they ha&e the same

elements in them. If set ' is eFual to set -,

then e&ery element in set ' belons to set -

and &ice &ersa. =e denote this by writin

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b. If either set ' or set - has at least one element

that is not common to both, then the sets are

said to be unequal and we write ' -.

6 Determine 0hether each o- the -ollo0ing )airs

o- sets are e&al or not.

*a+ A1263"3#5an7 F12#363"5

*'+ 1 2o77 n&m'ers 'et0een # an7 B5

< 1 2x:x G !3x is a )ositie n&m'er5

S 1 Hy:,$ Gy G 3y is an integer5

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*a+ $______ *-+ !_______< *'+JJJJJ> *g+ ,!._____S

*c+ ;_____< *h+ n(

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b. The 9enn diaram below shows the

relationship between set ' and set -.

ercise

#. Ising the sm'ols or or 3 -ill in the

'lanks o- the -ollo0ing statements. *a+ 2p,F,r5JJJJJ2l,m,p,F,r,s5

*'+ 2 5JJJJJ2x4 7" x !K5

*c+ 2 : ! #"x x 5____2#"3!3#35

*7+ 2)olgons5 _______ 2)entagons5

*e+ 2he)tagons5_______2)olgons5

*-+ 2$3#3"5_______2#3"3$5

*g+ 263345_____2 5

*h+ 2m&lti)les o- $5 ____ 2m&lti)les o- 65

*i+ 2m&lti)les o- 65 ____ 2m&lti)les o- $5

*(+ 2-actors o- $5 _____ 2-actors o- "5

*k+ 2-actors o- "5 _____ 2-actors o- $5

>t is gien that > an7 >

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*'+ A____ F____ C

*c+ A ____C

*7+ D____C

*e+ C____D

6otes47

a. 'n empty set is a subset of any set.b. E&ery set is a subset of itself.c. The subsets of set {a, b} are { }, {a}, {b} and {a,b}.

d. The number of subsets for a set with n elements is n.

Examplen()

6umber of subsets

x

*

4 >t is gien that A 1 2)3 3 r3 s5 an7 n*F+ 1 . *a+ List all the s&'sets o- A.

*'+ State the n&m'er o- s&'sets o- set F.

Eien that 1 2triangles53 :1 2isosceles triangles5 an7

5 1 2e&ilateral triangles53

*a+ 7ra0 a ?enn 7iagram to ill&strate the

relationshi) 'et0een:35 an7 3

*'+ name the t)e o- triangle that 0o&l7 'e

o&tsi7e the set 8L9

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