SlideShare une entreprise Scribd logo
1  sur  34
Télécharger pour lire hors ligne
Set Language and Notation
By Keartisak Monchit Mathematics Department Benchamaratrangsarit School
! " #
$ ! P
%& P '
{ 10}P prime numbers lessthan
{2,3,5,7}P
{ / , 10}P x x is prime x
( ) *
o { / a positive integer}N x x is +
o { 1,2,3,4,...}N $
1 , 3 , 0 , 5N N N N 1 belongs to N
A ( )n A
{ 2,4,6,...,20 }A ( ) 10n A
{ 1,2,3,4,... }B ( ) (infinity)n B
,* { ' '}S letters of the word book
$ S
- S
{ , , }S b o k
( ) 3n S
Page 2
. '% { 1, 1, 2, 2, 2, 3 } { 1, 2, 3 }
/ { 1, 2, 3, 4, 5 } { 4, 1, 5, 2, 3 }
,* { / 1 18 }A x x is an even number between and
$ A
- A
{ 2, 4, 6, 8, 10, 12, 14, 16 }A
( ) 8n S
,* 2 2 2 2 2
{ 1 , 2 , 3 , 4 , 5 }B
0 B 1
23 B 4
{ 1 , 4 , 9 , 16 , 25 }B 56 9 B
2
{ / ; 5 }B x x n n I and n
,* { 3 , 4 , 5 , 6 }T
1
3
T 1
23 T 4
( A B 7 A B * 3
$ { letters from the word 'parallel' }A
{ letters from the word 'apparel' }B
A B 1
A B '
Page 3
{ , , , , }A p a r l e
{ , , , , }B a p r e l
A B * A B
$ { x/x is a digit from the phone number 92883388 }C
{ x/x is a digit from the phone number 92382238 }D
C D 1
- 3 - { 2 , 4 , 6 , ... ,100 }A
{ 5 , 10 , 15 , ... ,1000 }B
{ x/x = 2n , n I 10 }C and x
2
{ x/x I 100 }D and x
{ 1 , 3 , 5 , ... }A
{ 1 , 4 , 9 , 16 , 25 , ... }B
{ x/x = 2n 1 , n I }C
2
{ x/x I 100 }D and x
!
" #
( & ( ) 0n
- 3 2 { / 2 5 }A x x I and x
{ / 2 10 }B x x I and x
{ / , 5 x<1 }C x x I x and
"
( + * U *
Page 4
' ,* { 1 , 2 , 3 , ... , 10 }U
{ x / x less than 5 }A
{ x / x is odd number }B
( { 1 , 2 , 3 , 4 }A
{ 1 , 3 , 5 , 7 , 9 }B
* A B A
B A B A B A B
A B A B A # B
A B
{ 3 , 5 , 7 } and { 1 , 3 , 5 , 7 , 9 }A B
A B A B
( and ( )A B A B A B
{ 1 , 3 , 5 , 7 , ... } and { x / x I }C D
C D C D
( and ( )C D C D C D
{ x / x is an even number } and { x / x is an integer }E F
E F E F
( and ( )E F E F E F
{ x / x is a root of (x 1)(x 3) = 0 } , { 1 , 2 , 3 , 4 }P Q
{ 4 , 3 , 2 , 1 } and S { 1 , 3 , 5 }R
8 P Q R
' { 1 , 3 }P
( and ( )P Q P Q P Q
and ( )Q R R Q Q R
and ( )P S P S P S
Page 5
$ % % 2 * A
/ 2* A A
9 A B B A A B
: A B B C A C
; A B x x A x B
" &
{ 1 , 2 }A
A ' , {1} , {2} , {1,2}
. A : 2
2
. A 9 2
2 < %
{ 1 , 3 , 5 }B
B ' , {1} , {3} , {5} , {1,3} , {1,5} , {3,5} , {1,3,5}
. B = 3
2
. B > 3
2 < %
{ 1 , {1} }C
C ' , {1} , {{1}} , {1,{1}}
. A : 2
2
. A 9 2
2 < %
{ a , b , c , d }D
D ' , {a} , {b} , ... ,{ a , b , c , d }
. D %? 4
2
. A %; 4
2 < %
! % . A 2n
( )n A n
/ . A 2n
<% ( )n A n
Page 6
#
,* A @ A ( )P A
A ( ) { / }P A x x A
{ 1 , 2 }A
A ' , {1} , {2} , {1,2}
( ) { , {1} , {2} , {1,2} }P A
{ 1 , 3 , 5 }B
B ' , {1} , {3} , {5} , {1,3} , {1,5} , {3,5} , {1,3,5}
( ) { , {1} , {3} , {5} , {1,3} , {1,5} , {3,5} , {1,3,5}}P B
{ 1 , {1} }C
C ' , {1} , {{1}} , {1,{1}}
( ) { , {1} , {{1}} , {1,{1}}}P C
{ }D
D ' , { }
( ) { , { }}P D
{ 0 , 1 , {2}}E
E ' , {0}, {1}, {{2}}, {0,1}, {0,{2}}, {1,{2}}, {0,1,{2}}
( ) { , {0}, {1}, {{2}}, {0,1}, {0,{2}}, {1,{2}}, {0,1,{2}}}P E
! ' { , }A a b ( ( ) { ,{ },{ },{ , }}P A a b a b
( ) { ,{ },{ }, }P A a b A
% ( )P A { } ( )P A
/ ( )A P A { } ( )A P A
9 ( )x P A x A
: ( ) ( )P A PP A ( ) ( )PP A PPP A
; A B ( ) ( )P A P B
Page 7
(
( A B A B
A B A B
{ / }A B x x A or x B
$ {1,2,3,4,5}A {2,4,6,8,10}B {4,5,6,7,8}C
( {1,2,3,4,5,6,8,10}A B
{1,2,3,4,5,6,7,8}A C
{2,4,5,6,7,8,10}B C
$ {1,3,5,7,9}A {2,4,6,8,10}B {1,2,3,4,...,10}C
( {1,2,3,4,5,6,7,8,9,10}A B C
{1,2,3,4,5,6,7,8,9,10}A C C
{1,2,3,4,5,6,7,8,9,10}B C C
$ { / }A x x I { / }B x x I {0}C
( { / 0}A B x x I and x
{ / 0}A C x x I and x
{ / 0}B C x x I and x
# % A A
/ A A A
9 A U U
: A B B A *$
; ( ) ( )A B C A B C A B C
* $
Page 8
? A B A B B
> A B A B
= A B A B
0 A B A C B C
%& A A B A B C
( A B A B
A B
{ / }A B x x A and x B
$ {1,2,3,4,5}A {2,4,6,8,10}B {4,5,6,7,8}C
( {2,4}A B
{4,5}A C
{4,6,8}B C
$ {1,3,5,7,9}A {2,4,6,8,10}B {1,2,3,4,...,10}C
( A B
{1,3,5,7,9}A C A
{2,4,6,8,10}B C B
$ { / }A x x I { / }B x x I {0}C
( A B
A C
B C
Page 9
# 1. A
2. A A A
3. A U A
4. A B B A *$
5. ( ) ( )A B C A B C A B C * $
6. if and only ifA B A B A
7. if and only of and are disjoint setsA B A B
8. If thenA B A C B C
9. andA B A A B C A B
10. if and only ifA B A B A B
11. ( ) ( ) ( )A B C A B A C 8 *$
12. ( ) ( ) ( )A B C A B A C 8 *$
) ( A A
A * U
{ / }A x x U and x A
$ {1,2,3,4,5,6,7,8}U {4,6,8}A {1,3,5,7}B
( {1,2,3,5,7}A
{2,4,6,8}B
( ) {2}A B
( )A B U
U
( ) {4,6,8}A A
( ) {1,3,5,7}B B
Page 10
$ { / }U x x I * { / }A x x I { / }B x x I {0}C
( { / 0} {0}A x x I or x I
{ / 0} {0}B x x I or x I
( ) {0}A B
( )A B U
{ / 0}C x x I and x
$ {1,2,3,4,5,6,7,8}U {4,6,8}A {1,3,5,7}B
( {1,2,3,5,7}A {2,4,6,8}B
( ) {2}A B ( )A B U
{2}A B {1,2,3,4,5,6,7,8}A B U
! ( )A B A B ( )A B A B
# % U
/ U
9 A A U
: A A
; ( )A A (( ) )A A
? A B B A
> ( )A B A B 8 A $
= ( )A B A B 8 A $
( A B A B
A B
{ / }A B x x A and x B
{ / }B A x x B and x A
Page 11
$ {1,2,3,4,5,6,7}A * {5,6,7,8,9,10}B {11,12,13}C
( {1,2,3,4}A B
{8,9,10}B A
{1,2,3,4,5,6,7}A C A
{5,6,7,8,9,10}B C B
$ {1,3,5,7,9}A {1,2,3,4,5,6,7,8,9,10}B
( A B
{2,4,6,8,10}B A
! ' A B A B
# % U A A
/ A A A
9 A B B A 3 A B
: A B A B
; A B A B
? ( )A B A A B
> A B B A
= ( ) ( ) ( )A B C A B A C
0 ( ) ( ) ( )A B C A B A C
%& ( ) ( ) ( )A B C A C B C
%% ( ) ( ) ( )A B C A C B C
+ ,
B *
*
A B + * :
Page 12
C A B
C A B
C A
C A B
Exercise
% 8 B 8
% ( ) ( ) ( )A B C A B A C
/ ( ) ( ) ( )A B C A B A C
A A A
C C C
B B B
A A A
C C C
B B B
Page 13
9 ( )A B A B
: ( )A B A B
; ( ) ( ) ( )A B C A B A C
? ( ) ( ) ( )A B C A B A C
/ ,* B 8 D
%
/
9
:
;
?
>
=
A A A
C C C
B B B
A A A
C C C
B B B
A A A
C C C
B B B
A A A
C C C
B B B
A B
C
U
1
2
34
5
6
7
8
Page 14
!
,*
% A B ( ) ( ) ( )n A B n A n B
/ A B B C A C ( ) ( ) ( ) ( )n A B C n A n B n C
9 A B ( ) ( ) ( ) ( )n A B n A n B n A B
: A B B C A C
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )n A B C n A n B n C n A B n B C n A C n A B C
; ( ) ( ) ( )n A n U n A
? ( ) ( ) ( )n A B n A n A B
A B
A
B
C
A B
A B
C
A
A
A B
Page 15
,* , , ( ) 100 , ( ) 60 , ( ) 75 ( ) 45A U B U n U n A n B and n A B
-
% ( )n A B / ( )n A B 9 ( )n A B
: ( )n A B ; ( )n B A ? ( )n A
> ( )n B = ( )n A B 0 ( )n B A
,* , , , ( ) 100 , ( ) 29 , ( ) 23 , ( ) 18A U B U C U n U n A n B n C
( ) 15 , ( ) 10 , ( ) 9 ( ) 6n A B n A C n B C and n A B C
-
% ( )n A B / ( )n B C 9 ( )n A C
: ( )n A B ; ( )n A B C ? ( )n A B C
> ( )n A B C = ( )n A B C
A B
U
A B
C
Page 16
Exercise
% ,* + *
( ) 150 , ( ) 62 , ( ) 55 ( ) 11n U n A n B and n A B -
% % ( )n A B % / ( )n A B
% 9 ( )n A B % : ( )n A B
% ; ( )n B A % ? ( )n A
% > ( )n B % = ( )n A B
% 0 ( )n B A % %& ( )n A B
/ ,* + *
( ) 50 , ( ) 6 , ( ) 38 ( ) ( )n U n A B n A B and n A n B -
/ % ( )n A / / ( )n A
/ 9 ( )n A B / : ( )n B A
/ ; ( )n A B / ? ( )n A B
/ > ( )n A B / = ( )n B A
/ 0 ( )n A B / %& ( )n B A
A B
U
A B
U
Page 17
9 ,* + *
( ) 80 , ( ) 35 , ( ) 28 , ( ) 21 , ( ) 12 , ( ) 10n U n A n B n C n A B n B C
( ) 14 ( ) 4n A C and n A B C -
9 % ( )n A B 9 / ( )n B C
9 9 ( )n A C 9 : ( )n A B C
9 ; ( )n A B 9 ? ( )n B C
9 > ( )n A C 9 = ( )n A B C
9 0 ( )n A B 9 %& ( )n B C
9 %% ( )n A C 9 %/ ( )n A B C
9 %9 ( )n A B 9 %: ( )n B C
9 %; ( )n C A 9 %? ( )n A B C
9 %> ( )n A C B 9 %= ( )n B C A
9 %0 ( )n A B C 9 /& ( )n B A C
A B
C
U
Page 18
Page 19
Page 20
Page 21
Page 22
Page 23
Exercise 1 : Sets and notation
Mathematics Department / Benchamaratrangsarit School
Name ………………………..……..……. No. ………. Class ….……
-& &
% ( * * %&
EEEEEEEEEEEEEEEEEEEEEEEEEE EE
/ ( !
EEEEEEEEEEEEEEEEEEEEEEEEEE EE
9 ( *
EEEEEEEEEEEEEEEEEEEEEEEEEE EE
: ( * < %&
EEEEEEEEEEEEEEEEEEEEEEEEEE EE
; ( < ; ;
EEEEEEEEEEEEEEEEEEEEEEEEEE EE
.& &
% 2
{ / 25 }x x I and x EEEEEEEEEEEEEE
/ { / 2 }x x n and n I EEEEEEEEEEEEEE
9 { / 5}x x I and x EEEEEEEEEEEEEE
: 3
{ / , 5}x x n n I and n EEEEEEEEEEEEEE
; 2
{ / 25 }x x I and x EEEEEEEEEEEEEE
/& &
% { 1 , 2 , 3 , 4 ,...} EEEEEEEEEEEEEE
/ { 1 , 1 } EEEEEEEEEEEEEE
9 { 1 , 2 , 3 , 4 , 5 } EEEEEEEEEEEEEE
: { sun , mon , tue , wed , thu , fri , sat } EEEEEEEEEEEEEE
; { 3, 6, 9, 12,...} EEEEEEEEEEEEEE
? { 1, 3, 5, 7, 9,...} EEEEEEEEEEEEEE
> { 1, 8, 27, 64,...} EEEEEEEEEEEEEE
= { 5, 10, 15, 20,..., 100 } EEEEEEEEEEEEEE
Page 24
Exercise 2 : Sets and notation
Mathematics Department / Benchamaratrangsarit School
Name ………………………..……..……. No. ………. Class ….……
-& &
% " / : = %? E %&/: # EEEEEEEEEEEEEE
/ " % 9 ; > E# EEEEEEEEEEEEEE
9 " / : ? " = %&%/ E# %&/: # EEEEEEEEEEEEEE
: " " # "" ## """ ### E# EEEEEEEEEEEEEE
; " 3 <
F 3 G% # EEEEEEEEEEEEEE
? " 3 F 3 H%&# EEEEEEEEEEEEEE
> " 3 F 3/
H%&&#
= " &% / " % / # " 9 : ; E# #
0 " 3 F 3 I/ H%&#
%& " 3 F 3 I4 ; . H;&#
%% " 3 .F 3 H&# EEEEEEEEEEEEEE
%/ " 3 F 3/
H%&#
%9 " 3 F 3 H% 3 G; #
%: " 3 F 3 I9
.#
%; " 3 .F 93 4 % I&#
%? " 3 @F 3 #
%> " 3 F 3/
4 /3 J % I&#
%= " 3 .F 3 G%& 3 H; #
%0 " "%# "% /# "% / 9# E#
/& " 3 @F 93 4 %; I&#
.& 0 1 &
{ / 2 5 }x x I and x
Page 25
Exercise 3 : Sets and notation
Mathematics Department / Benchamaratrangsarit School
Name ………………………..……..……. No. ………. Class ….……
# - &
% " 3 F % H3 %&# " / 9 : E %&# EEEEEEE
/ " 3 F 3/
4 3 I&# " 3 .F 3 4 % I&# EEEEEEE
9 " 3 F 3 I/ 4 % .# " % 9 ; > E# EEEEEEE
: " 3 F 3 I/ # " / : ? = E# EEEEEEE
; " 3 F 3 I 9
.# " % = /> ?: E# EEEEEEE
? " 3 .F 3/
I% # " % 4 % # EEEEEEE
> " 3 F 3/
H%&# " &% / 9 # EEEEEEE
= " 3 F 3 H% 3 G; # " # EEEEEEE
0 " 3 F 3 I/ J % .# " % 9 ; E# EEEEEEE
%& " # " # EEEEEEE
# . &
2" 34- * . * /* 5* 1* 6* 7* 8* 9* -:;
% I" 3 F 3 J / H= # ( IEEEEEEEE
/ I" 3 F 3 J / G> # ( IEEEEEEEE
9 I" 3 F 3/
J % I%&# ( IEEEEEEEE
: 8I" 3 F 3/
J / H/&# ( 8IEEEEEEEE
; 2I" 3 F 3 J / I3 4 / # ( 2IEEEEEEEE
2" 34 < " " ;
? -I" 3 F /3 H9&# ( -IEEEEEEEE
> ,I" 3 F 3 # ( ,IEEEEEEEE
= 6I" 3 F 3/
J % H/&# ( 6IEEEEEEEE
0 I" 3 F 3 J / I/ J 3 # ( IEEEEEEEE
%& KI" 3 F 3 7 %&# ( KIEEEEEEEE
Page 26
Exercise 4 : Sets and notation
Mathematics Department / Benchamaratrangsarit School
Name ………………………..……..……. No. ………. Class ….……
# - &
% " % 9 ; # " % / 9 : E %&#
/ " &/ : # " 3 F 3 .#
9 " ; %&%; /&# " % / 9 E %&&#
: " # " & " ##
; " % / 9 #
# . * &
% I" % 9 # ( @ IEEEEEEEEEEEEEE
/ I" &/ # ( @ IEEEEEEEEEEEEEE
9 I" # ( @ IEEEEEEEEEEEEEE
: 8I" % # ( @8 IEEEEEEEEEEEEEE
; 2I ( @2 IEEEEEEEEEEEEEE
? I" "%# # ( @ IEEEEEEEEEEEEEE
> I" % "%## ( @ IEEEEEEEEEEEEEE
= I" % # ( @ IEEEEEEEEEEEEEE
0 8I" % 9 ; # ( @8 IEEEEEEEEEEEEEE
%& 2I" " ## ( @2 IEEEEEEEEEEEEEE
Page 27
Exercise 5 : Sets and notation
Mathematics Department / Benchamaratrangsarit School
Name ………………………..……..……. No. ………. Class ….……
# - = 0* 2" = 0 &
.
% " % / 9 # " % 9 ; > #
/ " ; ? > # " % / 9 E %&#
9 " 3 F 3 G;# " 3 F 3 G%&#
: " % / 9 # " 9 / % #
; " 3 F 3 .# " 3 F 3 #
# . = 0* 2" = 0 &
.
% " % / 9 : # " / : ? = %&#
/ " 9 ; > # " % / 9 E %&#
9 " 3 F 3 G9 # " 3 F 3 G= #
: " % / 9 # " 9 / % #
; " 3 F 3 .# " 3 F 3 #
# / # >= 0* = 0?
Page 28
Exercise 6 : Sets and notation
Mathematics Department / Benchamaratrangsarit School
Name ………………………..……..……. No. ………. Class ….……
# - A * 2" A U &
A U A
% " % / 9 # " % / 9 E %&#
/ " / : ? = # " % / 9 E %&#
9 " 3 F 3 G; # " 3 F 3 .#
: " < % < / < 9 E# " 3 F 3 #
; " 3 F 3 .# " 3 F 3 #
? " 3 F 3 J
# " 3 F 3 #
> "&# " 3 F 3 #
= " 3 F 3 <
&# " 3 F 3 #
# . =, 0 * 2" = 0 &
4
% " % / 9 : # " : ; ? #
/ " ; ? > = # " / : ? #
9 " % / 9 E %&# " > = 0 #
: " : ; ? # " > = 0 %&%% #
; " 3 F 3 .# " 3 F 3 #
# /# ) >A A B ?
Page 29
Exercise 7 : Sets and notation
Mathematics Department / Benchamaratrangsarit School
Name ………………………..……..……. No. ………. Class ….……
# - + &
% / 4
9 4 :
; L
# . @ &
% / 9
EEEEEEEEE EEEEEEEEE EEEEEEEEE
: ;
EEEEEEEEE EEEEEEEEE
# / &
% / < 9 < <
B
A
B
A
B
A
B
A
B
A
A
B
B
AA
B
AB
AA
B
A
Page 30
Exercise 8 : Sets and notation
Mathematics Department / Benchamaratrangsarit School
Name ………………………..……..……. No. ………. Class ….……
ABCDEFGHIDJKLMNOPQDRJBSBTUVWJBXWIBDWJYZUM[
% MNOPQRSMTUVWTMXYWZR;&[MV]PQRSM[^_`abc`Qd9&[M V]PQRSMebfbVNWOgf/&[M
MNOPQRSMhRYiZjV]PQRSMhNkWcVWl_b; [M mnioUljb
MNOPQRSMhRYV]PQRSMhNkWcVWl_bZR [M A 2
MNOPQRSMhRYV][^_`abc`QdVSjbWPoRSlZR [M
MNOPQRSMhRYV]ebfbVNWOgfVSjbWPoRSlZR [M
/ MNOPQRSMZ : TUVWTMXYWZR:; [MV]PpjMqr`]Vp/; [M V]PpjM]bcPO`]Vp/&[M
V]PpjMhNkWqr`]Vpspn]bcPO`]Vp%&[M mnioUljb
MNOPQRSMhRYV]PpjMqr`]VpVSjbWPoRSlZR [M -
MNOPQRSMhRYiZjV]PpjMhNkWcVWVSjbWZR [M
9 OtbTMomtbMlMcZb_OuVW spn PhjbON]9& /; spn= `bZptboN]
mnioUljb mtbMlMcZb_OuVW PhjbON]
mtbMlMcZb_OuVW 4 PhjbON]
vTU shMmtbMlMcZb_OuVWPw`
: mbOQxyhRYOtbTMovTU + I%/& I;& I:; I:& I%&
I= I> spn I; mnioUljb
IEEEEEEE
z4 {IEEEEEEE
; mbOuUVhRY: L
IEEEEEEE +
z 4 {IEEEEEE
Page 31
Exercise 9 : Sets and notation
Mathematics Department / Benchamaratrangsarit School
Name ………………………..……..……. No. ………. Class ….……
ABCDEFGHIDJKLMNOPQDRJBSBTUVWJBXWIBDWJYZUM[
DJULMN- % OtbTMo + I=& I9; I:& I%&
mnioUljb % % IEEE
% / L
IEEE
/ OtbTMo + I%&& I9= I:/ I>9
mnioUljb % % IEEE
% / 4 IEEE
% 9 4 L
IEEEE
DJULMN. % OtbTMomtbMlMcZb_OuVWPw` spn Py|M %/ %? spn/=
`bZptboN]
mnioUljbmtbMlMcZb_OuVW 4 PhjbON]
mtbMlMcZb_OuVW 4 PhjbON]
/ mbOObQcV]}bZMNOPQRSMmtbMlM=&[MhRYV]PQRSM[^_`abc`QdTQ~V[VZ•_lP`VQd
•]ljbZRMNOPQRSMhRYV]PQRSM[^_`abc`Qd:; [M spnZRMNOPQRSMhRYV]PQRSM
[VZ•_lP`VQd;/ [M
mnioUljbMNOPQRSMhRYV]PQRSMhNkW[^_`abc`Qdspn[VZ•_lP`VQdZR [M
MNOPQRSMhRYV]PQRSM[^_`abc`QdP•RSWVSjbWPoRSlZR [M
MNOPQRSMhRYV]PQRSM[VZ•_lP`VQdP•RSWVSjbWPoRSlZR [M
Page 32
Exercise 10 : Sets and notation
Mathematics Department / Benchamaratrangsarit School
Name ………………………..……..……. No. ………. Class ….……
ABCDEFGHIDJKLMNOPQDRJBSBTUVWJBXWIBDWJYZUM[
DJULMN- % OtbTMo + I%&& I:& I;& I/&
mnioUljb % % IEEE
% / L
IEEE
/ OtbTMo I%%& I?& I:; I:&
I/& I%; I%&
mnioUljb / % I
/ / z < {I
/ 9 z < {I
DJULMN. vMObQcV]uVWMNOPQRSMNkMZN€SZaXOfb`VMypbSTUVWTMXYW•]ljb
9> [McV]•jbMl_b[^_`abc`Qd
:= [McV]•jbMl_bcNW[ZaXOfb A
:; [McV]•jbMl_bebfbihS
%; [McV]•jbMl_b[^_`abc`QdspncNW[ZaXOfb (
%9 [McV]•jbMl_bcNW[ZaXOfbspnebfbihS
> [McV]•jbMl_b[^_`abc`QdspnebfbihS
; [McV]•jbMhNkW 9 l_b
mnioUljb % MNOPQRSMPuUbcV]hNkWTZo [M : cV]•jbM[^_`abc`QdVSjbWPoRSl [M
/ cV]•jbMP•RSW / l_bZR [M ; cV]•jbM[^_`abc`QdspnebfbihS
9 cV]•jbMP•RSWl_bPoRSlZR [M P•RSW / l_bZR [M
Page 33
Post Test : Sets and notation
Mathematics Department / Benchamaratrangsarit School
Name ………………………..……..……. No. ………. Class ….……
ABCSJQGHIDJKLMNOPQDRJBLMN]^_C`MaBbRJC_MaX
% vTU I" < / < % &% / # PZ~YVPuRSMPw`
s]]]VOPW~YVMiu mn`QWON]uUVvo
O " 3 F 3 spn< 9 H3 H9 #
u " 3 F 3 spn3 H9 #
[ " 3 F 3 .spn3 < / #
W " 3 F 3 .spn3/
H; #
/ •_mbQ^buUV[lbZ`jViyMRk
% " % / 9 # I" 3 F 3 spn3/
H%&#
/ " / : ? E# I" 3 F 3 I/ J
#
uUVvo`jViyMRk}xO`UVW
O Py|MmQ_WhNkWcVWuUV
u Py|MPh‚mhNkWcVWuUV
[ Py|MmQ_WPĥbnuUV% PhjbMNkM
W Py|MmQ_WPĥbnuUV/ PhjbMNkM
9 uUV[lbZ`jViyMRkuUVvo}xO`UVW
O " 3 CF 3 G; spn3 H% # Py|MPw`
ljbWspnPw`mtbONo
u "% / " 9 : E## Py|MPw`VMNM`d
[ " 3 CF %H3 H; # Py|MPw`mtbONo
W " % / 9 # " % / 9 : E#
: vTU I" &% / "9 :# ";# "? > E##
uUVvo`jViyMRkiZj}xO`UVW
O " % / #
u " &% / #
[ " 9 : #
W ""? > E##
; vTU I" % / 9 : # I" / : ? = #
spn I" : ; ? # uUVvoiZj}xO`UVW
O I" % / 9 : ? = #
u I" / : #
[ 4 I" % / 9 = #
W 4 I" % / 9 ; ? #
? uUV[lbZvo`jViyMRkiZj}xO`UVW
O 4 4 I 4 4
u spn O‚`jVPZ~YV I
[ }Ub spUl I
W }Ub spUl I
> }Ub I spUl 4 PhjbON]uUVvo
O u
[ W 4
= OtbTMo I"% /# spUl@ `QWON]uUVvo
O " "%# "/# #
u ""%# "/# "% /##
[ " "%# "/# "% /##
W " "% /##
0 mtbMlMcZb_OuVW PhjbON]
/&9&spn; `bZptboN]mtbMlMcZb_OuVW
Py|MPhjbvo
O %; u :; [ ;& W ;;
%&mbOuUV0 mtbMlMcZb_O 4 Py|MPhjbvo
O /; u /&
[ %; W 9&
Page 34

Contenu connexe

Tendances

第2回 基本演算,データ型の基礎,ベクトルの操作方法
第2回 基本演算,データ型の基礎,ベクトルの操作方法第2回 基本演算,データ型の基礎,ベクトルの操作方法
第2回 基本演算,データ型の基礎,ベクトルの操作方法Wataru Shito
 
เฉลยMetrix1
เฉลยMetrix1เฉลยMetrix1
เฉลยMetrix1Noir Black
 
Handbook of Business Model Innovation
Handbook of Business Model InnovationHandbook of Business Model Innovation
Handbook of Business Model InnovationHochschule Ruhr West
 
เฉลยข้อสอบเมทริกซ์ ตอนที่ 2
เฉลยข้อสอบเมทริกซ์  ตอนที่ 2เฉลยข้อสอบเมทริกซ์  ตอนที่ 2
เฉลยข้อสอบเมทริกซ์ ตอนที่ 2K'Keng Hale's
 
第4回 データフレームの基本操作 その2
第4回 データフレームの基本操作 その2第4回 データフレームの基本操作 その2
第4回 データフレームの基本操作 その2Wataru Shito
 
Sistemas de comunicacion 4ta edicion - bruce a. carlson solutions manual
Sistemas de comunicacion   4ta edicion - bruce a. carlson solutions manualSistemas de comunicacion   4ta edicion - bruce a. carlson solutions manual
Sistemas de comunicacion 4ta edicion - bruce a. carlson solutions manualluis hernando rodriguez montenegro
 
第5回 様々なファイル形式の読み込みとデータの書き出し
第5回 様々なファイル形式の読み込みとデータの書き出し第5回 様々なファイル形式の読み込みとデータの書き出し
第5回 様々なファイル形式の読み込みとデータの書き出しWataru Shito
 
第6回 関数とフロー制御
第6回 関数とフロー制御第6回 関数とフロー制御
第6回 関数とフロー制御Wataru Shito
 
ข้อสอบMetrix
ข้อสอบMetrixข้อสอบMetrix
ข้อสอบMetrixNoir Black
 
第3回 データフレームの基本操作 その1
第3回 データフレームの基本操作 その1第3回 データフレームの基本操作 その1
第3回 データフレームの基本操作 その1Wataru Shito
 
ข้อสอบ Pat 1 + เฉลย
ข้อสอบ Pat 1 +  เฉลยข้อสอบ Pat 1 +  เฉลย
ข้อสอบ Pat 1 + เฉลยAunJan
 
MANUAL PINNACLE STUDIO ULTIMATE
MANUAL PINNACLE STUDIO ULTIMATEMANUAL PINNACLE STUDIO ULTIMATE
MANUAL PINNACLE STUDIO ULTIMATEautonomo
 

Tendances (15)

第2回 基本演算,データ型の基礎,ベクトルの操作方法
第2回 基本演算,データ型の基礎,ベクトルの操作方法第2回 基本演算,データ型の基礎,ベクトルの操作方法
第2回 基本演算,データ型の基礎,ベクトルの操作方法
 
เฉลยMetrix1
เฉลยMetrix1เฉลยMetrix1
เฉลยMetrix1
 
Handbook of Business Model Innovation
Handbook of Business Model InnovationHandbook of Business Model Innovation
Handbook of Business Model Innovation
 
เฉลยข้อสอบเมทริกซ์ ตอนที่ 2
เฉลยข้อสอบเมทริกซ์  ตอนที่ 2เฉลยข้อสอบเมทริกซ์  ตอนที่ 2
เฉลยข้อสอบเมทริกซ์ ตอนที่ 2
 
第4回 データフレームの基本操作 その2
第4回 データフレームの基本操作 その2第4回 データフレームの基本操作 その2
第4回 データフレームの基本操作 その2
 
Sistemas de comunicacion 4ta edicion - bruce a. carlson solutions manual
Sistemas de comunicacion   4ta edicion - bruce a. carlson solutions manualSistemas de comunicacion   4ta edicion - bruce a. carlson solutions manual
Sistemas de comunicacion 4ta edicion - bruce a. carlson solutions manual
 
第5回 様々なファイル形式の読み込みとデータの書き出し
第5回 様々なファイル形式の読み込みとデータの書き出し第5回 様々なファイル形式の読み込みとデータの書き出し
第5回 様々なファイル形式の読み込みとデータの書き出し
 
第6回 関数とフロー制御
第6回 関数とフロー制御第6回 関数とフロー制御
第6回 関数とフロー制御
 
ข้อสอบMetrix
ข้อสอบMetrixข้อสอบMetrix
ข้อสอบMetrix
 
第3回 データフレームの基本操作 その1
第3回 データフレームの基本操作 その1第3回 データフレームの基本操作 その1
第3回 データフレームの基本操作 その1
 
Key pat1 1-53
Key pat1 1-53Key pat1 1-53
Key pat1 1-53
 
ข้อสอบ Pat 1 + เฉลย
ข้อสอบ Pat 1 +  เฉลยข้อสอบ Pat 1 +  เฉลย
ข้อสอบ Pat 1 + เฉลย
 
MANUAL PINNACLE STUDIO ULTIMATE
MANUAL PINNACLE STUDIO ULTIMATEMANUAL PINNACLE STUDIO ULTIMATE
MANUAL PINNACLE STUDIO ULTIMATE
 
Homologação monitores 2012
Homologação monitores 2012Homologação monitores 2012
Homologação monitores 2012
 
Key pat1 3-52 math
Key pat1 3-52 mathKey pat1 3-52 math
Key pat1 3-52 math
 

Similaire à Set language and notation

TDS Rules, 2023 উৎসে কর বিধিমালা, ২০২৩
TDS Rules, 2023 উৎসে কর বিধিমালা, ২০২৩ TDS Rules, 2023 উৎসে কর বিধিমালা, ২০২৩
TDS Rules, 2023 উৎসে কর বিধিমালা, ২০২৩ Sazzad Hossain, ITP, MBA, CSCA™
 
TDS Tax Deducted at Source Rule 2023 এস.আর.ও. নং ২০৬-২১০-আইন-২০২৩
TDS Tax Deducted at Source Rule 2023 এস.আর.ও. নং ২০৬-২১০-আইন-২০২৩TDS Tax Deducted at Source Rule 2023 এস.আর.ও. নং ২০৬-২১০-আইন-২০২৩
TDS Tax Deducted at Source Rule 2023 এস.আর.ও. নং ২০৬-২১০-আইন-২০২৩Sazzad Hossain, ITP, MBA, CSCA™
 
التفاضل و التكامل
التفاضل و التكاملالتفاضل و التكامل
التفاضل و التكاملمحمد الجمل
 
Наибольшая общая мера: 2500 лет
Наибольшая общая мера: 2500 летНаибольшая общая мера: 2500 лет
Наибольшая общая мера: 2500 летsixtyone
 
Алексей Калиниченко "Интеллектуальная собственность и механизм правового регу...
Алексей Калиниченко "Интеллектуальная собственность и механизм правового регу...Алексей Калиниченко "Интеллектуальная собственность и механизм правового регу...
Алексей Калиниченко "Интеллектуальная собственность и механизм правового регу...Бизнес-инкубатор
 
Safe Reinforcement Learning
Safe Reinforcement LearningSafe Reinforcement Learning
Safe Reinforcement LearningDongmin Lee
 
PRML エビデンス近似 3.5 3.6.1
PRML エビデンス近似  3.5 3.6.1PRML エビデンス近似  3.5 3.6.1
PRML エビデンス近似 3.5 3.6.1tmtm otm
 
33-EJERCICIOS-DE-CD-Y-CI (1).pdf
33-EJERCICIOS-DE-CD-Y-CI (1).pdf33-EJERCICIOS-DE-CD-Y-CI (1).pdf
33-EJERCICIOS-DE-CD-Y-CI (1).pdfssuserf577d6
 
Kubernetes ネットワーキングのすべて
Kubernetes ネットワーキングのすべてKubernetes ネットワーキングのすべて
Kubernetes ネットワーキングのすべてLINE Corporation
 
Doa dan-dzikir-pilihan
Doa dan-dzikir-pilihanDoa dan-dzikir-pilihan
Doa dan-dzikir-pilihanRidas Zabbarae
 
2. csi rebate process workshop october 2010 long-1
2. csi rebate process workshop   october 2010 long-12. csi rebate process workshop   october 2010 long-1
2. csi rebate process workshop october 2010 long-1moeshahram
 

Similaire à Set language and notation (20)

1 teste 5ano1
1 teste 5ano11 teste 5ano1
1 teste 5ano1
 
Determinacion minimos cuadrados
Determinacion minimos cuadradosDeterminacion minimos cuadrados
Determinacion minimos cuadrados
 
Xadrez
XadrezXadrez
Xadrez
 
OpenSSO Microsoft Interop
OpenSSO Microsoft InteropOpenSSO Microsoft Interop
OpenSSO Microsoft Interop
 
TDS Rules, 2023 উৎসে কর বিধিমালা, ২০২৩
TDS Rules, 2023 উৎসে কর বিধিমালা, ২০২৩ TDS Rules, 2023 উৎসে কর বিধিমালা, ২০২৩
TDS Rules, 2023 উৎসে কর বিধিমালা, ২০২৩
 
TDS Tax Deducted at Source Rule 2023 এস.আর.ও. নং ২০৬-২১০-আইন-২০২৩
TDS Tax Deducted at Source Rule 2023 এস.আর.ও. নং ২০৬-২১০-আইন-২০২৩TDS Tax Deducted at Source Rule 2023 এস.আর.ও. নং ২০৬-২১০-আইন-২০২৩
TDS Tax Deducted at Source Rule 2023 এস.আর.ও. নং ২০৬-২১০-আইন-২০২৩
 
التفاضل و التكامل
التفاضل و التكاملالتفاضل و التكامل
التفاضل و التكامل
 
O anticristo
O anticristoO anticristo
O anticristo
 
Наибольшая общая мера: 2500 лет
Наибольшая общая мера: 2500 летНаибольшая общая мера: 2500 лет
Наибольшая общая мера: 2500 лет
 
Алексей Калиниченко "Интеллектуальная собственность и механизм правового регу...
Алексей Калиниченко "Интеллектуальная собственность и механизм правового регу...Алексей Калиниченко "Интеллектуальная собственность и механизм правового регу...
Алексей Калиниченко "Интеллектуальная собственность и механизм правового регу...
 
Safe Reinforcement Learning
Safe Reinforcement LearningSafe Reinforcement Learning
Safe Reinforcement Learning
 
Salah Prez Cogifactory
Salah Prez CogifactorySalah Prez Cogifactory
Salah Prez Cogifactory
 
H-Academy
H-AcademyH-Academy
H-Academy
 
PRML エビデンス近似 3.5 3.6.1
PRML エビデンス近似  3.5 3.6.1PRML エビデンス近似  3.5 3.6.1
PRML エビデンス近似 3.5 3.6.1
 
33-EJERCICIOS-DE-CD-Y-CI (1).pdf
33-EJERCICIOS-DE-CD-Y-CI (1).pdf33-EJERCICIOS-DE-CD-Y-CI (1).pdf
33-EJERCICIOS-DE-CD-Y-CI (1).pdf
 
Kubernetes ネットワーキングのすべて
Kubernetes ネットワーキングのすべてKubernetes ネットワーキングのすべて
Kubernetes ネットワーキングのすべて
 
Doa dan-dzikir-pilihan
Doa dan-dzikir-pilihanDoa dan-dzikir-pilihan
Doa dan-dzikir-pilihan
 
36thchapter
36thchapter36thchapter
36thchapter
 
الإستاتيكا
الإستاتيكاالإستاتيكا
الإستاتيكا
 
2. csi rebate process workshop october 2010 long-1
2. csi rebate process workshop   october 2010 long-12. csi rebate process workshop   october 2010 long-1
2. csi rebate process workshop october 2010 long-1
 

Plus de Aon Narinchoti

บทคัดย่อ
บทคัดย่อบทคัดย่อ
บทคัดย่อAon Narinchoti
 
รายละเอียดชุมนุมคณิตศาสตร์ออนไลน์
รายละเอียดชุมนุมคณิตศาสตร์ออนไลน์รายละเอียดชุมนุมคณิตศาสตร์ออนไลน์
รายละเอียดชุมนุมคณิตศาสตร์ออนไลน์Aon Narinchoti
 
ส่งตีพิมพ์ มสธ
ส่งตีพิมพ์ มสธส่งตีพิมพ์ มสธ
ส่งตีพิมพ์ มสธAon Narinchoti
 
Lxt6 sonvyqi20150807080936
Lxt6 sonvyqi20150807080936Lxt6 sonvyqi20150807080936
Lxt6 sonvyqi20150807080936Aon Narinchoti
 
ตารางฟังก์ชันตรีโกณมิติ
ตารางฟังก์ชันตรีโกณมิติตารางฟังก์ชันตรีโกณมิติ
ตารางฟังก์ชันตรีโกณมิติAon Narinchoti
 
การใช้หลักปรัชญาเศรษฐกิจพอเพียง
การใช้หลักปรัชญาเศรษฐกิจพอเพียงการใช้หลักปรัชญาเศรษฐกิจพอเพียง
การใช้หลักปรัชญาเศรษฐกิจพอเพียงAon Narinchoti
 
คำอธิบายรายวิชา
คำอธิบายรายวิชาคำอธิบายรายวิชา
คำอธิบายรายวิชาAon Narinchoti
 
อัตราส่วนคะแนน
อัตราส่วนคะแนนอัตราส่วนคะแนน
อัตราส่วนคะแนนAon Narinchoti
 

Plus de Aon Narinchoti (20)

บทคัดย่อ
บทคัดย่อบทคัดย่อ
บทคัดย่อ
 
Prob
ProbProb
Prob
 
Event
EventEvent
Event
 
Sample space
Sample spaceSample space
Sample space
 
Random experiment
Random experimentRandom experiment
Random experiment
 
His brob
His brobHis brob
His brob
 
รายละเอียดชุมนุมคณิตศาสตร์ออนไลน์
รายละเอียดชุมนุมคณิตศาสตร์ออนไลน์รายละเอียดชุมนุมคณิตศาสตร์ออนไลน์
รายละเอียดชุมนุมคณิตศาสตร์ออนไลน์
 
Wordpress
WordpressWordpress
Wordpress
 
ส่งตีพิมพ์ มสธ
ส่งตีพิมพ์ มสธส่งตีพิมพ์ มสธ
ส่งตีพิมพ์ มสธ
 
Lxt6 sonvyqi20150807080936
Lxt6 sonvyqi20150807080936Lxt6 sonvyqi20150807080936
Lxt6 sonvyqi20150807080936
 
Know5
Know5Know5
Know5
 
ตารางฟังก์ชันตรีโกณมิติ
ตารางฟังก์ชันตรีโกณมิติตารางฟังก์ชันตรีโกณมิติ
ตารางฟังก์ชันตรีโกณมิติ
 
Know4
Know4Know4
Know4
 
Know3
Know3Know3
Know3
 
Know2
Know2Know2
Know2
 
Know1
Know1Know1
Know1
 
การใช้หลักปรัชญาเศรษฐกิจพอเพียง
การใช้หลักปรัชญาเศรษฐกิจพอเพียงการใช้หลักปรัชญาเศรษฐกิจพอเพียง
การใช้หลักปรัชญาเศรษฐกิจพอเพียง
 
Climometer
ClimometerClimometer
Climometer
 
คำอธิบายรายวิชา
คำอธิบายรายวิชาคำอธิบายรายวิชา
คำอธิบายรายวิชา
 
อัตราส่วนคะแนน
อัตราส่วนคะแนนอัตราส่วนคะแนน
อัตราส่วนคะแนน
 

Dernier

Holdier Curriculum Vitae (April 2024).pdf
Holdier Curriculum Vitae (April 2024).pdfHoldier Curriculum Vitae (April 2024).pdf
Holdier Curriculum Vitae (April 2024).pdfagholdier
 
How to Manage Global Discount in Odoo 17 POS
How to Manage Global Discount in Odoo 17 POSHow to Manage Global Discount in Odoo 17 POS
How to Manage Global Discount in Odoo 17 POSCeline George
 
Introduction to Nonprofit Accounting: The Basics
Introduction to Nonprofit Accounting: The BasicsIntroduction to Nonprofit Accounting: The Basics
Introduction to Nonprofit Accounting: The BasicsTechSoup
 
FSB Advising Checklist - Orientation 2024
FSB Advising Checklist - Orientation 2024FSB Advising Checklist - Orientation 2024
FSB Advising Checklist - Orientation 2024Elizabeth Walsh
 
Salient Features of India constitution especially power and functions
Salient Features of India constitution especially power and functionsSalient Features of India constitution especially power and functions
Salient Features of India constitution especially power and functionsKarakKing
 
ICT role in 21st century education and it's challenges.
ICT role in 21st century education and it's challenges.ICT role in 21st century education and it's challenges.
ICT role in 21st century education and it's challenges.MaryamAhmad92
 
Unit-IV- Pharma. Marketing Channels.pptx
Unit-IV- Pharma. Marketing Channels.pptxUnit-IV- Pharma. Marketing Channels.pptx
Unit-IV- Pharma. Marketing Channels.pptxVishalSingh1417
 
Kodo Millet PPT made by Ghanshyam bairwa college of Agriculture kumher bhara...
Kodo Millet  PPT made by Ghanshyam bairwa college of Agriculture kumher bhara...Kodo Millet  PPT made by Ghanshyam bairwa college of Agriculture kumher bhara...
Kodo Millet PPT made by Ghanshyam bairwa college of Agriculture kumher bhara...pradhanghanshyam7136
 
Vishram Singh - Textbook of Anatomy Upper Limb and Thorax.. Volume 1 (1).pdf
Vishram Singh - Textbook of Anatomy  Upper Limb and Thorax.. Volume 1 (1).pdfVishram Singh - Textbook of Anatomy  Upper Limb and Thorax.. Volume 1 (1).pdf
Vishram Singh - Textbook of Anatomy Upper Limb and Thorax.. Volume 1 (1).pdfssuserdda66b
 
Making communications land - Are they received and understood as intended? we...
Making communications land - Are they received and understood as intended? we...Making communications land - Are they received and understood as intended? we...
Making communications land - Are they received and understood as intended? we...Association for Project Management
 
Application orientated numerical on hev.ppt
Application orientated numerical on hev.pptApplication orientated numerical on hev.ppt
Application orientated numerical on hev.pptRamjanShidvankar
 
TỔNG ÔN TẬP THI VÀO LỚP 10 MÔN TIẾNG ANH NĂM HỌC 2023 - 2024 CÓ ĐÁP ÁN (NGỮ Â...
TỔNG ÔN TẬP THI VÀO LỚP 10 MÔN TIẾNG ANH NĂM HỌC 2023 - 2024 CÓ ĐÁP ÁN (NGỮ Â...TỔNG ÔN TẬP THI VÀO LỚP 10 MÔN TIẾNG ANH NĂM HỌC 2023 - 2024 CÓ ĐÁP ÁN (NGỮ Â...
TỔNG ÔN TẬP THI VÀO LỚP 10 MÔN TIẾNG ANH NĂM HỌC 2023 - 2024 CÓ ĐÁP ÁN (NGỮ Â...Nguyen Thanh Tu Collection
 
Explore beautiful and ugly buildings. Mathematics helps us create beautiful d...
Explore beautiful and ugly buildings. Mathematics helps us create beautiful d...Explore beautiful and ugly buildings. Mathematics helps us create beautiful d...
Explore beautiful and ugly buildings. Mathematics helps us create beautiful d...christianmathematics
 
HMCS Max Bernays Pre-Deployment Brief (May 2024).pptx
HMCS Max Bernays Pre-Deployment Brief (May 2024).pptxHMCS Max Bernays Pre-Deployment Brief (May 2024).pptx
HMCS Max Bernays Pre-Deployment Brief (May 2024).pptxEsquimalt MFRC
 
How to Give a Domain for a Field in Odoo 17
How to Give a Domain for a Field in Odoo 17How to Give a Domain for a Field in Odoo 17
How to Give a Domain for a Field in Odoo 17Celine George
 
Understanding Accommodations and Modifications
Understanding  Accommodations and ModificationsUnderstanding  Accommodations and Modifications
Understanding Accommodations and ModificationsMJDuyan
 
Food safety_Challenges food safety laboratories_.pdf
Food safety_Challenges food safety laboratories_.pdfFood safety_Challenges food safety laboratories_.pdf
Food safety_Challenges food safety laboratories_.pdfSherif Taha
 
Unit-IV; Professional Sales Representative (PSR).pptx
Unit-IV; Professional Sales Representative (PSR).pptxUnit-IV; Professional Sales Representative (PSR).pptx
Unit-IV; Professional Sales Representative (PSR).pptxVishalSingh1417
 
Python Notes for mca i year students osmania university.docx
Python Notes for mca i year students osmania university.docxPython Notes for mca i year students osmania university.docx
Python Notes for mca i year students osmania university.docxRamakrishna Reddy Bijjam
 

Dernier (20)

Holdier Curriculum Vitae (April 2024).pdf
Holdier Curriculum Vitae (April 2024).pdfHoldier Curriculum Vitae (April 2024).pdf
Holdier Curriculum Vitae (April 2024).pdf
 
Mehran University Newsletter Vol-X, Issue-I, 2024
Mehran University Newsletter Vol-X, Issue-I, 2024Mehran University Newsletter Vol-X, Issue-I, 2024
Mehran University Newsletter Vol-X, Issue-I, 2024
 
How to Manage Global Discount in Odoo 17 POS
How to Manage Global Discount in Odoo 17 POSHow to Manage Global Discount in Odoo 17 POS
How to Manage Global Discount in Odoo 17 POS
 
Introduction to Nonprofit Accounting: The Basics
Introduction to Nonprofit Accounting: The BasicsIntroduction to Nonprofit Accounting: The Basics
Introduction to Nonprofit Accounting: The Basics
 
FSB Advising Checklist - Orientation 2024
FSB Advising Checklist - Orientation 2024FSB Advising Checklist - Orientation 2024
FSB Advising Checklist - Orientation 2024
 
Salient Features of India constitution especially power and functions
Salient Features of India constitution especially power and functionsSalient Features of India constitution especially power and functions
Salient Features of India constitution especially power and functions
 
ICT role in 21st century education and it's challenges.
ICT role in 21st century education and it's challenges.ICT role in 21st century education and it's challenges.
ICT role in 21st century education and it's challenges.
 
Unit-IV- Pharma. Marketing Channels.pptx
Unit-IV- Pharma. Marketing Channels.pptxUnit-IV- Pharma. Marketing Channels.pptx
Unit-IV- Pharma. Marketing Channels.pptx
 
Kodo Millet PPT made by Ghanshyam bairwa college of Agriculture kumher bhara...
Kodo Millet  PPT made by Ghanshyam bairwa college of Agriculture kumher bhara...Kodo Millet  PPT made by Ghanshyam bairwa college of Agriculture kumher bhara...
Kodo Millet PPT made by Ghanshyam bairwa college of Agriculture kumher bhara...
 
Vishram Singh - Textbook of Anatomy Upper Limb and Thorax.. Volume 1 (1).pdf
Vishram Singh - Textbook of Anatomy  Upper Limb and Thorax.. Volume 1 (1).pdfVishram Singh - Textbook of Anatomy  Upper Limb and Thorax.. Volume 1 (1).pdf
Vishram Singh - Textbook of Anatomy Upper Limb and Thorax.. Volume 1 (1).pdf
 
Making communications land - Are they received and understood as intended? we...
Making communications land - Are they received and understood as intended? we...Making communications land - Are they received and understood as intended? we...
Making communications land - Are they received and understood as intended? we...
 
Application orientated numerical on hev.ppt
Application orientated numerical on hev.pptApplication orientated numerical on hev.ppt
Application orientated numerical on hev.ppt
 
TỔNG ÔN TẬP THI VÀO LỚP 10 MÔN TIẾNG ANH NĂM HỌC 2023 - 2024 CÓ ĐÁP ÁN (NGỮ Â...
TỔNG ÔN TẬP THI VÀO LỚP 10 MÔN TIẾNG ANH NĂM HỌC 2023 - 2024 CÓ ĐÁP ÁN (NGỮ Â...TỔNG ÔN TẬP THI VÀO LỚP 10 MÔN TIẾNG ANH NĂM HỌC 2023 - 2024 CÓ ĐÁP ÁN (NGỮ Â...
TỔNG ÔN TẬP THI VÀO LỚP 10 MÔN TIẾNG ANH NĂM HỌC 2023 - 2024 CÓ ĐÁP ÁN (NGỮ Â...
 
Explore beautiful and ugly buildings. Mathematics helps us create beautiful d...
Explore beautiful and ugly buildings. Mathematics helps us create beautiful d...Explore beautiful and ugly buildings. Mathematics helps us create beautiful d...
Explore beautiful and ugly buildings. Mathematics helps us create beautiful d...
 
HMCS Max Bernays Pre-Deployment Brief (May 2024).pptx
HMCS Max Bernays Pre-Deployment Brief (May 2024).pptxHMCS Max Bernays Pre-Deployment Brief (May 2024).pptx
HMCS Max Bernays Pre-Deployment Brief (May 2024).pptx
 
How to Give a Domain for a Field in Odoo 17
How to Give a Domain for a Field in Odoo 17How to Give a Domain for a Field in Odoo 17
How to Give a Domain for a Field in Odoo 17
 
Understanding Accommodations and Modifications
Understanding  Accommodations and ModificationsUnderstanding  Accommodations and Modifications
Understanding Accommodations and Modifications
 
Food safety_Challenges food safety laboratories_.pdf
Food safety_Challenges food safety laboratories_.pdfFood safety_Challenges food safety laboratories_.pdf
Food safety_Challenges food safety laboratories_.pdf
 
Unit-IV; Professional Sales Representative (PSR).pptx
Unit-IV; Professional Sales Representative (PSR).pptxUnit-IV; Professional Sales Representative (PSR).pptx
Unit-IV; Professional Sales Representative (PSR).pptx
 
Python Notes for mca i year students osmania university.docx
Python Notes for mca i year students osmania university.docxPython Notes for mca i year students osmania university.docx
Python Notes for mca i year students osmania university.docx
 

Set language and notation

  • 1. Set Language and Notation By Keartisak Monchit Mathematics Department Benchamaratrangsarit School ! " # $ ! P %& P ' { 10}P prime numbers lessthan {2,3,5,7}P { / , 10}P x x is prime x ( ) * o { / a positive integer}N x x is + o { 1,2,3,4,...}N $ 1 , 3 , 0 , 5N N N N 1 belongs to N A ( )n A { 2,4,6,...,20 }A ( ) 10n A { 1,2,3,4,... }B ( ) (infinity)n B ,* { ' '}S letters of the word book $ S - S { , , }S b o k ( ) 3n S
  • 2. Page 2 . '% { 1, 1, 2, 2, 2, 3 } { 1, 2, 3 } / { 1, 2, 3, 4, 5 } { 4, 1, 5, 2, 3 } ,* { / 1 18 }A x x is an even number between and $ A - A { 2, 4, 6, 8, 10, 12, 14, 16 }A ( ) 8n S ,* 2 2 2 2 2 { 1 , 2 , 3 , 4 , 5 }B 0 B 1 23 B 4 { 1 , 4 , 9 , 16 , 25 }B 56 9 B 2 { / ; 5 }B x x n n I and n ,* { 3 , 4 , 5 , 6 }T 1 3 T 1 23 T 4 ( A B 7 A B * 3 $ { letters from the word 'parallel' }A { letters from the word 'apparel' }B A B 1 A B '
  • 3. Page 3 { , , , , }A p a r l e { , , , , }B a p r e l A B * A B $ { x/x is a digit from the phone number 92883388 }C { x/x is a digit from the phone number 92382238 }D C D 1 - 3 - { 2 , 4 , 6 , ... ,100 }A { 5 , 10 , 15 , ... ,1000 }B { x/x = 2n , n I 10 }C and x 2 { x/x I 100 }D and x { 1 , 3 , 5 , ... }A { 1 , 4 , 9 , 16 , 25 , ... }B { x/x = 2n 1 , n I }C 2 { x/x I 100 }D and x ! " # ( & ( ) 0n - 3 2 { / 2 5 }A x x I and x { / 2 10 }B x x I and x { / , 5 x<1 }C x x I x and " ( + * U *
  • 4. Page 4 ' ,* { 1 , 2 , 3 , ... , 10 }U { x / x less than 5 }A { x / x is odd number }B ( { 1 , 2 , 3 , 4 }A { 1 , 3 , 5 , 7 , 9 }B * A B A B A B A B A B A B A B A # B A B { 3 , 5 , 7 } and { 1 , 3 , 5 , 7 , 9 }A B A B A B ( and ( )A B A B A B { 1 , 3 , 5 , 7 , ... } and { x / x I }C D C D C D ( and ( )C D C D C D { x / x is an even number } and { x / x is an integer }E F E F E F ( and ( )E F E F E F { x / x is a root of (x 1)(x 3) = 0 } , { 1 , 2 , 3 , 4 }P Q { 4 , 3 , 2 , 1 } and S { 1 , 3 , 5 }R 8 P Q R ' { 1 , 3 }P ( and ( )P Q P Q P Q and ( )Q R R Q Q R and ( )P S P S P S
  • 5. Page 5 $ % % 2 * A / 2* A A 9 A B B A A B : A B B C A C ; A B x x A x B " & { 1 , 2 }A A ' , {1} , {2} , {1,2} . A : 2 2 . A 9 2 2 < % { 1 , 3 , 5 }B B ' , {1} , {3} , {5} , {1,3} , {1,5} , {3,5} , {1,3,5} . B = 3 2 . B > 3 2 < % { 1 , {1} }C C ' , {1} , {{1}} , {1,{1}} . A : 2 2 . A 9 2 2 < % { a , b , c , d }D D ' , {a} , {b} , ... ,{ a , b , c , d } . D %? 4 2 . A %; 4 2 < % ! % . A 2n ( )n A n / . A 2n <% ( )n A n
  • 6. Page 6 # ,* A @ A ( )P A A ( ) { / }P A x x A { 1 , 2 }A A ' , {1} , {2} , {1,2} ( ) { , {1} , {2} , {1,2} }P A { 1 , 3 , 5 }B B ' , {1} , {3} , {5} , {1,3} , {1,5} , {3,5} , {1,3,5} ( ) { , {1} , {3} , {5} , {1,3} , {1,5} , {3,5} , {1,3,5}}P B { 1 , {1} }C C ' , {1} , {{1}} , {1,{1}} ( ) { , {1} , {{1}} , {1,{1}}}P C { }D D ' , { } ( ) { , { }}P D { 0 , 1 , {2}}E E ' , {0}, {1}, {{2}}, {0,1}, {0,{2}}, {1,{2}}, {0,1,{2}} ( ) { , {0}, {1}, {{2}}, {0,1}, {0,{2}}, {1,{2}}, {0,1,{2}}}P E ! ' { , }A a b ( ( ) { ,{ },{ },{ , }}P A a b a b ( ) { ,{ },{ }, }P A a b A % ( )P A { } ( )P A / ( )A P A { } ( )A P A 9 ( )x P A x A : ( ) ( )P A PP A ( ) ( )PP A PPP A ; A B ( ) ( )P A P B
  • 7. Page 7 ( ( A B A B A B A B { / }A B x x A or x B $ {1,2,3,4,5}A {2,4,6,8,10}B {4,5,6,7,8}C ( {1,2,3,4,5,6,8,10}A B {1,2,3,4,5,6,7,8}A C {2,4,5,6,7,8,10}B C $ {1,3,5,7,9}A {2,4,6,8,10}B {1,2,3,4,...,10}C ( {1,2,3,4,5,6,7,8,9,10}A B C {1,2,3,4,5,6,7,8,9,10}A C C {1,2,3,4,5,6,7,8,9,10}B C C $ { / }A x x I { / }B x x I {0}C ( { / 0}A B x x I and x { / 0}A C x x I and x { / 0}B C x x I and x # % A A / A A A 9 A U U : A B B A *$ ; ( ) ( )A B C A B C A B C * $
  • 8. Page 8 ? A B A B B > A B A B = A B A B 0 A B A C B C %& A A B A B C ( A B A B A B { / }A B x x A and x B $ {1,2,3,4,5}A {2,4,6,8,10}B {4,5,6,7,8}C ( {2,4}A B {4,5}A C {4,6,8}B C $ {1,3,5,7,9}A {2,4,6,8,10}B {1,2,3,4,...,10}C ( A B {1,3,5,7,9}A C A {2,4,6,8,10}B C B $ { / }A x x I { / }B x x I {0}C ( A B A C B C
  • 9. Page 9 # 1. A 2. A A A 3. A U A 4. A B B A *$ 5. ( ) ( )A B C A B C A B C * $ 6. if and only ifA B A B A 7. if and only of and are disjoint setsA B A B 8. If thenA B A C B C 9. andA B A A B C A B 10. if and only ifA B A B A B 11. ( ) ( ) ( )A B C A B A C 8 *$ 12. ( ) ( ) ( )A B C A B A C 8 *$ ) ( A A A * U { / }A x x U and x A $ {1,2,3,4,5,6,7,8}U {4,6,8}A {1,3,5,7}B ( {1,2,3,5,7}A {2,4,6,8}B ( ) {2}A B ( )A B U U ( ) {4,6,8}A A ( ) {1,3,5,7}B B
  • 10. Page 10 $ { / }U x x I * { / }A x x I { / }B x x I {0}C ( { / 0} {0}A x x I or x I { / 0} {0}B x x I or x I ( ) {0}A B ( )A B U { / 0}C x x I and x $ {1,2,3,4,5,6,7,8}U {4,6,8}A {1,3,5,7}B ( {1,2,3,5,7}A {2,4,6,8}B ( ) {2}A B ( )A B U {2}A B {1,2,3,4,5,6,7,8}A B U ! ( )A B A B ( )A B A B # % U / U 9 A A U : A A ; ( )A A (( ) )A A ? A B B A > ( )A B A B 8 A $ = ( )A B A B 8 A $ ( A B A B A B { / }A B x x A and x B { / }B A x x B and x A
  • 11. Page 11 $ {1,2,3,4,5,6,7}A * {5,6,7,8,9,10}B {11,12,13}C ( {1,2,3,4}A B {8,9,10}B A {1,2,3,4,5,6,7}A C A {5,6,7,8,9,10}B C B $ {1,3,5,7,9}A {1,2,3,4,5,6,7,8,9,10}B ( A B {2,4,6,8,10}B A ! ' A B A B # % U A A / A A A 9 A B B A 3 A B : A B A B ; A B A B ? ( )A B A A B > A B B A = ( ) ( ) ( )A B C A B A C 0 ( ) ( ) ( )A B C A B A C %& ( ) ( ) ( )A B C A C B C %% ( ) ( ) ( )A B C A C B C + , B * * A B + * :
  • 12. Page 12 C A B C A B C A C A B Exercise % 8 B 8 % ( ) ( ) ( )A B C A B A C / ( ) ( ) ( )A B C A B A C A A A C C C B B B A A A C C C B B B
  • 13. Page 13 9 ( )A B A B : ( )A B A B ; ( ) ( ) ( )A B C A B A C ? ( ) ( ) ( )A B C A B A C / ,* B 8 D % / 9 : ; ? > = A A A C C C B B B A A A C C C B B B A A A C C C B B B A A A C C C B B B A B C U 1 2 34 5 6 7 8
  • 14. Page 14 ! ,* % A B ( ) ( ) ( )n A B n A n B / A B B C A C ( ) ( ) ( ) ( )n A B C n A n B n C 9 A B ( ) ( ) ( ) ( )n A B n A n B n A B : A B B C A C ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )n A B C n A n B n C n A B n B C n A C n A B C ; ( ) ( ) ( )n A n U n A ? ( ) ( ) ( )n A B n A n A B A B A B C A B A B C A A A B
  • 15. Page 15 ,* , , ( ) 100 , ( ) 60 , ( ) 75 ( ) 45A U B U n U n A n B and n A B - % ( )n A B / ( )n A B 9 ( )n A B : ( )n A B ; ( )n B A ? ( )n A > ( )n B = ( )n A B 0 ( )n B A ,* , , , ( ) 100 , ( ) 29 , ( ) 23 , ( ) 18A U B U C U n U n A n B n C ( ) 15 , ( ) 10 , ( ) 9 ( ) 6n A B n A C n B C and n A B C - % ( )n A B / ( )n B C 9 ( )n A C : ( )n A B ; ( )n A B C ? ( )n A B C > ( )n A B C = ( )n A B C A B U A B C
  • 16. Page 16 Exercise % ,* + * ( ) 150 , ( ) 62 , ( ) 55 ( ) 11n U n A n B and n A B - % % ( )n A B % / ( )n A B % 9 ( )n A B % : ( )n A B % ; ( )n B A % ? ( )n A % > ( )n B % = ( )n A B % 0 ( )n B A % %& ( )n A B / ,* + * ( ) 50 , ( ) 6 , ( ) 38 ( ) ( )n U n A B n A B and n A n B - / % ( )n A / / ( )n A / 9 ( )n A B / : ( )n B A / ; ( )n A B / ? ( )n A B / > ( )n A B / = ( )n B A / 0 ( )n A B / %& ( )n B A A B U A B U
  • 17. Page 17 9 ,* + * ( ) 80 , ( ) 35 , ( ) 28 , ( ) 21 , ( ) 12 , ( ) 10n U n A n B n C n A B n B C ( ) 14 ( ) 4n A C and n A B C - 9 % ( )n A B 9 / ( )n B C 9 9 ( )n A C 9 : ( )n A B C 9 ; ( )n A B 9 ? ( )n B C 9 > ( )n A C 9 = ( )n A B C 9 0 ( )n A B 9 %& ( )n B C 9 %% ( )n A C 9 %/ ( )n A B C 9 %9 ( )n A B 9 %: ( )n B C 9 %; ( )n C A 9 %? ( )n A B C 9 %> ( )n A C B 9 %= ( )n B C A 9 %0 ( )n A B C 9 /& ( )n B A C A B C U
  • 23. Page 23 Exercise 1 : Sets and notation Mathematics Department / Benchamaratrangsarit School Name ………………………..……..……. No. ………. Class ….…… -& & % ( * * %& EEEEEEEEEEEEEEEEEEEEEEEEEE EE / ( ! EEEEEEEEEEEEEEEEEEEEEEEEEE EE 9 ( * EEEEEEEEEEEEEEEEEEEEEEEEEE EE : ( * < %& EEEEEEEEEEEEEEEEEEEEEEEEEE EE ; ( < ; ; EEEEEEEEEEEEEEEEEEEEEEEEEE EE .& & % 2 { / 25 }x x I and x EEEEEEEEEEEEEE / { / 2 }x x n and n I EEEEEEEEEEEEEE 9 { / 5}x x I and x EEEEEEEEEEEEEE : 3 { / , 5}x x n n I and n EEEEEEEEEEEEEE ; 2 { / 25 }x x I and x EEEEEEEEEEEEEE /& & % { 1 , 2 , 3 , 4 ,...} EEEEEEEEEEEEEE / { 1 , 1 } EEEEEEEEEEEEEE 9 { 1 , 2 , 3 , 4 , 5 } EEEEEEEEEEEEEE : { sun , mon , tue , wed , thu , fri , sat } EEEEEEEEEEEEEE ; { 3, 6, 9, 12,...} EEEEEEEEEEEEEE ? { 1, 3, 5, 7, 9,...} EEEEEEEEEEEEEE > { 1, 8, 27, 64,...} EEEEEEEEEEEEEE = { 5, 10, 15, 20,..., 100 } EEEEEEEEEEEEEE
  • 24. Page 24 Exercise 2 : Sets and notation Mathematics Department / Benchamaratrangsarit School Name ………………………..……..……. No. ………. Class ….……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{ / 2 5 }x x I and x
  • 25. Page 25 Exercise 3 : Sets and notation Mathematics Department / Benchamaratrangsarit School Name ………………………..……..……. No. ………. Class ….……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
  • 26. Page 26 Exercise 4 : Sets and notation Mathematics Department / Benchamaratrangsarit School Name ………………………..……..……. No. ………. Class ….…… # - & % " % 9 ; # " % / 9 : E %&# / " &/ : # " 3 F 3 .# 9 " ; %&%; /&# " % / 9 E %&&# : " # " & " ## ; " % / 9 # # . * & % I" % 9 # ( @ IEEEEEEEEEEEEEE / I" &/ # ( @ IEEEEEEEEEEEEEE 9 I" # ( @ IEEEEEEEEEEEEEE : 8I" % # ( @8 IEEEEEEEEEEEEEE ; 2I ( @2 IEEEEEEEEEEEEEE ? I" "%# # ( @ IEEEEEEEEEEEEEE > I" % "%## ( @ IEEEEEEEEEEEEEE = I" % # ( @ IEEEEEEEEEEEEEE 0 8I" % 9 ; # ( @8 IEEEEEEEEEEEEEE %& 2I" " ## ( @2 IEEEEEEEEEEEEEE
  • 27. Page 27 Exercise 5 : Sets and notation Mathematics Department / Benchamaratrangsarit School Name ………………………..……..……. No. ………. Class ….…… # - = 0* 2" = 0 & . % " % / 9 # " % 9 ; > # / " ; ? > # " % / 9 E %&# 9 " 3 F 3 G;# " 3 F 3 G%&# : " % / 9 # " 9 / % # ; " 3 F 3 .# " 3 F 3 # # . = 0* 2" = 0 & . % " % / 9 : # " / : ? = %&# / " 9 ; > # " % / 9 E %&# 9 " 3 F 3 G9 # " 3 F 3 G= # : " % / 9 # " 9 / % # ; " 3 F 3 .# " 3 F 3 # # / # >= 0* = 0?
  • 28. Page 28 Exercise 6 : Sets and notation Mathematics Department / Benchamaratrangsarit School Name ………………………..……..……. No. ………. Class ….…… # - A * 2" A U & A U A % " % / 9 # " % / 9 E %&# / " / : ? = # " % / 9 E %&# 9 " 3 F 3 G; # " 3 F 3 .# : " < % < / < 9 E# " 3 F 3 # ; " 3 F 3 .# " 3 F 3 # ? " 3 F 3 J # " 3 F 3 # > "&# " 3 F 3 # = " 3 F 3 < &# " 3 F 3 # # . =, 0 * 2" = 0 & 4 % " % / 9 : # " : ; ? # / " ; ? > = # " / : ? # 9 " % / 9 E %&# " > = 0 # : " : ; ? # " > = 0 %&%% # ; " 3 F 3 .# " 3 F 3 # # /# ) >A A B ?
  • 29. Page 29 Exercise 7 : Sets and notation Mathematics Department / Benchamaratrangsarit School Name ………………………..……..……. No. ………. Class ….…… # - + & % / 4 9 4 : ; L # . @ & % / 9 EEEEEEEEE EEEEEEEEE EEEEEEEEE : ; EEEEEEEEE EEEEEEEEE # / & % / < 9 < < B A B A B A B A B A A B B AA B AB AA B A
  • 30. Page 30 Exercise 8 : Sets and notation Mathematics Department / Benchamaratrangsarit School Name ………………………..……..……. No. ………. Class ….…… ABCDEFGHIDJKLMNOPQDRJBSBTUVWJBXWIBDWJYZUM[ % MNOPQRSMTUVWTMXYWZR;&[MV]PQRSM[^_`abc`Qd9&[M V]PQRSMebfbVNWOgf/&[M MNOPQRSMhRYiZjV]PQRSMhNkWcVWl_b; [M mnioUljb MNOPQRSMhRYV]PQRSMhNkWcVWl_bZR [M A 2 MNOPQRSMhRYV][^_`abc`QdVSjbWPoRSlZR [M MNOPQRSMhRYV]ebfbVNWOgfVSjbWPoRSlZR [M / MNOPQRSMZ : TUVWTMXYWZR:; [MV]PpjMqr`]Vp/; [M V]PpjM]bcPO`]Vp/&[M V]PpjMhNkWqr`]Vpspn]bcPO`]Vp%&[M mnioUljb MNOPQRSMhRYV]PpjMqr`]VpVSjbWPoRSlZR [M - MNOPQRSMhRYiZjV]PpjMhNkWcVWVSjbWZR [M 9 OtbTMomtbMlMcZb_OuVW spn PhjbON]9& /; spn= `bZptboN] mnioUljb mtbMlMcZb_OuVW PhjbON] mtbMlMcZb_OuVW 4 PhjbON] vTU shMmtbMlMcZb_OuVWPw` : mbOQxyhRYOtbTMovTU + I%/& I;& I:; I:& I%& I= I> spn I; mnioUljb IEEEEEEE z4 {IEEEEEEE ; mbOuUVhRY: L IEEEEEEE + z 4 {IEEEEEE
  • 31. Page 31 Exercise 9 : Sets and notation Mathematics Department / Benchamaratrangsarit School Name ………………………..……..……. No. ………. Class ….…… ABCDEFGHIDJKLMNOPQDRJBSBTUVWJBXWIBDWJYZUM[ DJULMN- % OtbTMo + I=& I9; I:& I%& mnioUljb % % IEEE % / L IEEE / OtbTMo + I%&& I9= I:/ I>9 mnioUljb % % IEEE % / 4 IEEE % 9 4 L IEEEE DJULMN. % OtbTMomtbMlMcZb_OuVWPw` spn Py|M %/ %? spn/= `bZptboN] mnioUljbmtbMlMcZb_OuVW 4 PhjbON] mtbMlMcZb_OuVW 4 PhjbON] / mbOObQcV]}bZMNOPQRSMmtbMlM=&[MhRYV]PQRSM[^_`abc`QdTQ~V[VZ•_lP`VQd •]ljbZRMNOPQRSMhRYV]PQRSM[^_`abc`Qd:; [M spnZRMNOPQRSMhRYV]PQRSM [VZ•_lP`VQd;/ [M mnioUljbMNOPQRSMhRYV]PQRSMhNkW[^_`abc`Qdspn[VZ•_lP`VQdZR [M MNOPQRSMhRYV]PQRSM[^_`abc`QdP•RSWVSjbWPoRSlZR [M MNOPQRSMhRYV]PQRSM[VZ•_lP`VQdP•RSWVSjbWPoRSlZR [M
  • 32. Page 32 Exercise 10 : Sets and notation Mathematics Department / Benchamaratrangsarit School Name ………………………..……..……. No. ………. Class ….…… ABCDEFGHIDJKLMNOPQDRJBSBTUVWJBXWIBDWJYZUM[ DJULMN- % OtbTMo + I%&& I:& I;& I/& mnioUljb % % IEEE % / L IEEE / OtbTMo I%%& I?& I:; I:& I/& I%; I%& mnioUljb / % I / / z < {I / 9 z < {I DJULMN. vMObQcV]uVWMNOPQRSMNkMZN€SZaXOfb`VMypbSTUVWTMXYW•]ljb 9> [McV]•jbMl_b[^_`abc`Qd := [McV]•jbMl_bcNW[ZaXOfb A :; [McV]•jbMl_bebfbihS %; [McV]•jbMl_b[^_`abc`QdspncNW[ZaXOfb ( %9 [McV]•jbMl_bcNW[ZaXOfbspnebfbihS > [McV]•jbMl_b[^_`abc`QdspnebfbihS ; [McV]•jbMhNkW 9 l_b mnioUljb % MNOPQRSMPuUbcV]hNkWTZo [M : cV]•jbM[^_`abc`QdVSjbWPoRSl [M / cV]•jbMP•RSW / l_bZR [M ; cV]•jbM[^_`abc`QdspnebfbihS 9 cV]•jbMP•RSWl_bPoRSlZR [M P•RSW / l_bZR [M
  • 33. Page 33 Post Test : Sets and notation Mathematics Department / Benchamaratrangsarit School Name ………………………..……..……. No. ………. Class ….…… ABCSJQGHIDJKLMNOPQDRJBLMN]^_C`MaBbRJC_MaX % vTU I" < / < % &% / # PZ~YVPuRSMPw` s]]]VOPW~YVMiu mn`QWON]uUVvo O " 3 F 3 spn< 9 H3 H9 # u " 3 F 3 spn3 H9 # [ " 3 F 3 .spn3 < / # W " 3 F 3 .spn3/ H; # / •_mbQ^buUV[lbZ`jViyMRk % " % / 9 # I" 3 F 3 spn3/ H%&# / " / : ? E# I" 3 F 3 I/ J # uUVvo`jViyMRk}xO`UVW O Py|MmQ_WhNkWcVWuUV u Py|MPh‚mhNkWcVWuUV [ Py|MmQ_WPƒ•bnuUV% PhjbMNkM W Py|MmQ_WPƒ•bnuUV/ PhjbMNkM 9 uUV[lbZ`jViyMRkuUVvo}xO`UVW O " 3 CF 3 G; spn3 H% # Py|MPw` ljbWspnPw`mtbONo u "% / " 9 : E## Py|MPw`VMNM`d [ " 3 CF %H3 H; # Py|MPw`mtbONo W " % / 9 # " % / 9 : E# : vTU I" &% / "9 :# ";# "? > E## uUVvo`jViyMRkiZj}xO`UVW O " % / # u " &% / # [ " 9 : # W ""? > E## ; vTU I" % / 9 : # I" / : ? = # spn I" : ; ? # uUVvoiZj}xO`UVW O I" % / 9 : ? = # u I" / : # [ 4 I" % / 9 = # W 4 I" % / 9 ; ? # ? uUV[lbZvo`jViyMRkiZj}xO`UVW O 4 4 I 4 4 u spn O‚`jVPZ~YV I [ }Ub spUl I W }Ub spUl I > }Ub I spUl 4 PhjbON]uUVvo O u [ W 4 = OtbTMo I"% /# spUl@ `QWON]uUVvo O " "%# "/# # u ""%# "/# "% /## [ " "%# "/# "% /## W " "% /## 0 mtbMlMcZb_OuVW PhjbON] /&9&spn; `bZptboN]mtbMlMcZb_OuVW Py|MPhjbvo O %; u :; [ ;& W ;; %&mbOuUV0 mtbMlMcZb_O 4 Py|MPhjbvo O /; u /& [ %; W 9&