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(Relative Universe) Subsets

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Exercises 1.1Answer Page 7

Which of the following represent a pair of equal

1) A = {letters in the word “กรรมกร ” }B = {letters in the word “มรรคา ” }C = {letters in the word “มกราคม ” }D = {letters in the word “รากไม้ ” }

A ={ก,ร,ม }B ={ม,ร,ค }C ={ม,ก,ร,ค }D ={ร,ก,ม}

A = D

Exercises 1.1Answer Page 7

Which of the following represent a pair of equal

2) E = {7,14,21,…,343} F = {x:x = 7n , n is a natural number less than 50}

F = {7,14,21,…,343}

E = {7,14,21,…,343} E = F

Exercises 1.1Answer Page 7

Which of the following represent a pair of equal

},11:{)3 numbernaturalaisnn

xxA

,...}54,

43,

32,

21,0{B

,...}54,

43,

32,

21,0{A A = B

Exercises 1.1Answer Page 7

Which of the following represent a pair of equal

4) A= {1,2,3,4,5}B= {5,4,3,2,1}

A = B

Exercises 1.1Answer Page 8

Which of the following represent a pair of equal

5) C = {0,1,3,7}D = {x:x is a integer number lass than10}

D = {9,8,7,6,…} DC

Exercises 1.1Answer Page 8

Which of the following represent a pair of equal

6) E ={12,14,16,18}F ={14,16,12,18}

E = F

Exercises 1.1Answer Page 8

Which of the following represent a pair of equal

7) K= {x:x is a even number less than 10}L = {2,4,6,8}

K = {8,6,4,2,0,-2,-4,…}FE

Exercises 1.1Answer Page 8

Which of the following represent a pair of equal

36:{)8 2 xandIntegeraisxxM

}6{N

}6,6{M

NM

1.2 ( Relative Universe)

The universal set is the set of all the elements Under a certain discussion

The symbol U is used to represent an universal set

Example

The universal set of A = { 2 , 4 , 6 , 8 }

U = {x:x is a even number}

Example

The universal set of B = {apples, durian,coconut} could be

U = {All fruits}

Example

The universal set of C = {tables , chairs,cuboard,drawer} could be U = {All furniture}

(Subsets)If each member of set A is also a member of set B , then set A is a subset of set BExampleA = {0, 1}, B = {0, 1, 2} and C = {0, 1, {1}}A C But B C A B

Given

(Power set)Power set is a group of all possible subset of agiven setThe collection of all subsets of a set “A” is called“the power set of A” It is representd as P(A)

ExampleA ={1,2,3}

Then P(A) =

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

A= { a , b }

Thus,there are 4 subset altogether

{a} , {b} , {a,b} ,

Example

B= { 2,4,6 }

Thus,there are 8 subset altogether

{2} , {4} , {6} , {2,4} , {2,6} , {4,6} , {2,4,6} ,

Example

T= { a,b,c,d }

Thus,there are 16 subset altogether

{a} , {b} , {c} , {d} , {a,b} , {a,c} , {a,d} ,

{a,b,c} , {a,b,d} ,

{b,c,d} , {a,b,c,d} ,

{b,c} , {b,d} , {c,d} , {a,c,d} ,

Example

T= { 1,{2},3, }

Thus,there are 16 subset altogether

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

{1,{2},3} ,

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

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

Example

E= { {a} , b }

Thus,there are 4 subset altogether

{{a}} ,{b} , {{a},b} ,

Example

B= { 1,7,8 }

Thus,there are 8 subset altogether

{1} , {7} , {8} , {1,7} , {1,8} , {7,8} , {1,7,8} ,

Example

Exercises 1.3Home work Page 12

1. Geven A = {2,{4,5},4} each of the follwing is True (T) or False (F)

A}5,4){1

A}5,4){2

A}}5,4){{3

A5)4

A}5){5A}5){6

Exercises 1.3Home work Page 12

2. Write down all the subset Each of the following

3. Write down Power set Each of the following

1.{1} 2.{1,2} 3.{-1,0,1}

1.{5} 2.{0,1} 3.{2,3,4}

Exercises 1.3Home work Page 12

4. Given A = {1,2,3,4} Write the subset from one element , and two elements

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Teacher Mr.Chaweng

Stand SW 100

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