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
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