The document discusses sets and their properties. It defines sets like A={m,p,r,w}, B={2,1,0,1,2}, and C={2,3,5}. It calculates properties of sets like the number of elements (n(A)=4, n(B)=5, n(C)=3). It also discusses power sets and their sizes compared to the original sets, like P(A) having 16 elements while A only has 4. Subsets, proper subsets, and empty/null sets are also covered.

1. O-NET / A-NET 11
{s,e,t}
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(Set) ,
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360 ,
(Element
Member)
A, B, C
{ } A , B
7, C 360 , D
7, E 3 33
A { , , , , , , }
(comma)
B { 2, 1, 0, 1, 2} B {0, 1, 1, 2, 2}
C {2, 3, 5} D {2, 3, 5} C D
( 360 2 2 2 3 3 5)
E {4, 5, 6, 7, ..., 32}
“...”
Math E-Book Release 2.2 ( )

2. O-NET / A-NET 12
(Finite S ¨u´·Õè¼i´ºoÂ! S
Set) “ A” n (A)
e«µµo仹ÕÁÕ¨íҹǹÊÁÒªi¡e·Òã´
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n (A) 7, n (B) 5, n (C) 3, { , 0, 1, {2, 3},(4, 5)}
n (E) 29 ¤íÒµoº¤×o 5 µaÇ ä´æ¡ e«µÇÒ§, eÅ¢ 0,
(Null Set Empty Set) { } eÅ¢ 1, e«µ {2,3}, æÅ¤Ùoa¹´aº (4,5)
¹a蹤×oe«µ¹aºe»¹ 1 ¤Ùoa¹´aº¹aºe»¹ 1
n( ) 0
{(1, 2), (2, 1), {1, 2}, {2, 1}}
¤íÒµoº¤×o 3 µaÇ ä´æ¡ ¤Ùoa¹´aº (1,2), ¤Ù
(Infinite Set) F 2, oa¹´aº (2,1), æÅe«µ {1,2}
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1-2 ¡aºe«µ 2-1 ¶×oÇÒeËÁ×o¹¡a¹æÅäÁ
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e«µ¨íÒ¡a´¤Ãaº ¶Ö§æÁ¨íҹǹÊÁÒªi¡¨´ÙÇÒ
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ÁÒ¡¢¹Ò´ä˹ 浡çäÁÁÒ¡¶Ö§o¹a¹µ¹..
“ ” 2 B, 3 C , 0.5 G
“ ” 2.5 B, 4 C, 0 G
(Relative Universe) U
U U
U { 2, 1, 0, 0.5, 7} H {x | x > 0} H {0, 0.5, 7}
U H {0, 1, 2, 3, ...}
U (R)
H {x | x > 0} H {x R | x > 0}
1.1
(Subset) B A
B A ( B A
B A) “B A” B A
“B A” B A
A {m, p, r, w}
B B A 16
{m} {p} {r} {w}
S ¢oÊa§e¡µ! S
{m, p} {m, r} {m, w} {p, r} {p, w} {r, w} »Ã¤ {a, b} A
{m, p, r} {m, p, w} {m, r, w} {p, r, w} ÁÕ¤ÇÒÁËÁÒÂÇÒ a A æÅ b A
{m, p, r, w}
Math E-Book Release 2.2 ( )

3. O-NET / A-NET 13
1. A
2. A A
3. n 2n ... ( 24 16 )
4. (Proper Subset) 2n 1
( )
( A A A A ) ...
(Power Set)
A P(A)
n S ¢oÊa§e¡µ! S
A n P(A) 2
A {m, p, r, w} »Ã¤ {a, b} P(A)
P (A) { , {m}, {p}, {r}, {w}, {m, p}, {m, r}, ..., {m, p, r, w} } ÁÕ¤ÇÒÁËÁÒÂÇÒ {a, b} A
¹a蹤×o a A æÅ b A
( 16 16.3)
n n!
n r r (n r)! r !
x! 1 2 3 ... x
7 3
7 7! 1 2 3 4 5 6 7
35
3 4! 3! 1 2 3 4 1 2 3
S ¨u´·Õè¼i´ºoÂ! S
. A {a}
¹o§ Áa¡¨ÊaºÊ¹ÃËÇÒ§ ¡aº { }
21 2 {a} ÇÒµÒ§¡a¹oÂÒ§äà ...
P (A) { , {a}}
(e«µÇÒ§) e»ÃÕºeÊÁ×o¹¡Åo§e»ÅÒ äÁ
. B {a, b} ÁÕoäÃoÂÙã¹¹aé¹eÅ (¨íҹǹÊÁÒªi¡e·Ò¡aº 0)
22 4 , {a} , {b} {a, b} ¨e¢Õ¹Êa Åa¡É³e»¹ { } ¡çä´
P (B) { , {a}, {b}, {a, b}} 浶ҶÒÁÇÒ¡Åo§ãºË¹Ö觫Öè§ÁÕ¡Åo§e»ÅÒoÕ¡
. C {2, 3, 5} ãºoÂ٢ҧ㹠¹aºe»¹¡Åo§ÇÒ§e»ÅÒËÃ×oäÁ
23 8 , {2} , {3} , {5} , {2, 3} , ¤íÒµoº¡ç¤×oäÁe»ÅÒæÅÇãªäËÁ¤Ãaº
{2, 5} {3, 5}
, {2, 3, 5} ¡çeËÁ×o¹¡a¹¡aº e«µ¢o§e«µÇÒ§ { }
P (C) { , {2}, {3}, {5}, {2, 3}, {2, 5}, {3, 5}, {2, 3, 5}} «Öè§äÁä´e»¹e«µÇÒ§oÕ¡µoä»æÅÇ ...
ËÃ×o¶ÒµoºÊaé¹ ¡ç¤×o n( ) 0
. D
æµ n({ }) 1
20 1 P (D) { }
Math E-Book Release 2.2 ( )

4. O-NET / A-NET 14
E { , {0}, { }} P(E)
{ , { }, {{0}}, {{ }}, { , {0}}, { , { }}, {{0}, { }}, { , {0}, { }}}
A, B A {1, 3, 5, 7} B {1, 2, 3, 4, 5, 6, 7}
. X X P (A)
X P (A) X A
X 2 4 16
4 4 4 4 4
1 4 6 4 1 16
0 1 2 3 4
. X X P (A) n (X) < 2
X P (A) X A 16 ( .) n (X) < 2
4 4 4
1 4 6 11
0 1 2
( )
. Y A Y Y B
A Y 1, 3, 5, 7 Y ... Y B
2, 4, 6 Y ( 1, 3, 5, 7
Y B ) ... 2, 4, 6 Y
3
{2, 4, 6} 2 8
1.1
(1) A, B A B A B x A y B
(1.1) {x} B (1.3) {A} {B}
(1.2) {y} A (1.4) {A} {B}
(2) A {{ }, a, b, {a}, {a, b}}
(2.1) { } A (2.3) {{a}, b} A
(2.2) { } A (2.4) {a, b} A {a, b} A
(3)
(3.1) A B B C A C
(3.2) A B B C A C
(3.3) A B B C A C
Math E-Book Release 2.2 ( )

5. O-NET / A-NET 15
(4) A
(4.1) { x | x A} {A} (4.3) { x | {x} A} {A}
(4.2) { x | x A} A (4.4) { x | {x} }
(5)
(5.1) n (A) 5 A 32
(5.2) n (A) 5 A 32
(5.3) n (A) 5 A 32
(5.4) n (A) 5 A 32
(6) A 511 A
511 5
(7)
(7.1) (7.5) P( )
(7.2) (7.6) P( )
(7.3) { } (7.7) { } P( )
(7.4) { } (7.8) { } P( )
(8) A { , a, {b}, {a, b}}
(8.1) P (A) (8.6) a P (A)
(8.2) { } P (A) (8.7) {a} P (A)
(8.3) P (A) (8.8) {b} P (A)
(8.4) { } P (A) (8.9) {{b}} P (A)
(8.5) { , a, {b}} P (A) (8.10) { , a, {b}} P (A)
(9) A { , 1, 2, 3, {1}, {1, 2}, {1, 2, 3}}
(9.1) { , {1}, {1, 2}} P (A) (9.3) {{1}, {2}, {3}} P (A)
(9.2) { , {1}, {1, 2}} P (A) (9.4) {{1}, {2}, {3}} P (A)
(10) [Ent’39] S {1, 2, 3, 4, 5, 6, 7} n (X) n (Y)
X {A P (S) | 1 A 7 A}
Y {A X| A 6}
1.2 -
S ¨u´·Õè¼i´ºoÂ! S
(Venn-Euler Diagram) ¤ÇèÇÒ´æ¼¹ÀÒ¾e«µ A æÅ B ã¹æºº
U ·aèÇä» ¤×oãËÁÕÊÁÒªi¡ÃÇÁ¡a¹¡o¹
( ) (eËÁ×o¹¡aºÃÙ»¡ÅÒ§) æÅǨҡ¹aé¹eÁ×èo·ÃÒº
A, B, C ÇÒªié¹Êǹã´äÁÁÕÊÁÒªi¡ ¤o¢մËÃ×oæÃe§Ò
·ié§ä».. ·íÒ溺¹Õéo¡Òʼi´¨¹oÂŧ¤Ãaº..
Math E-Book Release 2.2 ( )

6. O-NET / A-NET 16
U U U
A
A B A B B
A B A B A B
A {0, 1, 2, 3, 4} U
B {1, 3, 5, 7, 9} 04 1 9 B
A
C {2, 3, 5, 7, 11} 2 3 57
11
C
1. (Union : ) ... A B A B
U U U
A
A B A B B
A B B
2. (Intersection : ) ... A B A B
AB ( )
U U U
A
A B A B B
A B A B A
3. (Complement : ' ) U
A' A
A c
A A
4. (Difference Relative Complement : )
B A B A ... B A B A'
B A “ B A”
U U U
A
A B A B B
n (B A) n (B) n (A) n (B A) n (B) n (A B)
Math E-Book Release 2.2 ( )

7. O-NET / A-NET 17
A (B C) (A B) (A C) (A B) ' A' B'
A (B C) (A B) (A C) (A B) ' A' B'
A (B C) (A B) (A C) P (A) P (B) P (A B)
A (B C) (A B) (A C) P (A) P (B) P (A B)
A B A cup B A B A cap B
A, B A {1, 3, 5, 7} B {1, 2, 3, 4, 5, 6, 7}
( . . )
. Y A Y Y B
(A Y B ) ... A Y
1, 3, 5, 7 Y ( A Y )
{1, 3, 5, 7}
4
2 1 15 ...
Y B 2, 4, 6 Y (
1, 3, 5, 7 Y B ) ... 23 8
...
15 8 120
. Z {1, 2, 3} Z Z A
. ... {1, 2, 3} Z 1, 3 Z
( A Z ) 2 Z
(Z A ) ... 22 1 3 ...
Z A 5, 7 Z (
1, 3 Z A ) ... 22 4
...
3 4 12
. Z {1, 2, 3} Z Z A
{1, 2, 3} Z 1, 2, 3 Z
Z A 5, 7 Z (
Z Z A ) ...
22 4
Math E-Book Release 2.2 ( )

8. O-NET / A-NET 18
C { , { }, 0, {{ }, 0}, { , {0}}, {{ , {0}}}}
. n (P (C))
n (C) 6 n (P (C)) 26 64
. n (P (C) C)
n (P (C) C) 64 6 58 ... C
P (C) n (P (C) C) C P (C)
“ ”(
) ... { } “ ”
C ( C ) “ ”
C ... 0 “ ” !...
{{ }, 0} “ ” C ( )
“ ” { } C 0 C ... { , {0}} “ ” {0} C ...
{{ , {0}}} “ ” { , {0}} C C
( )
C P (C) 4 n (P (C) C) 64 4 60
. n (C P (C))
n (C P (C)) 6 64 ... P (C) C
. 4 n (C P (C)) 4 ...
n (C P (C)) 6 4 2
( .) n (C) 6 n (P (C)) 64 2 4 60
. n (C P (C)) 4
( .) n (C P (C)) 2 ( .) n (P (C) C) 60 C P(C)
. n [(P (C) C) (C P (C))]
. .( ) 60 2 62
( )
1.2
(11) A B {0, 1, 2, 3, 4, 5} A B {1, 3, 5} B C {2, 3, 5}
A C {0, 1, 2, 3, 5} A C {0, 3, 5}
. A B' {0} . B C' {1} . A C' {1} . B A' {2, 4}
(12) C' B'
U {x I | 1 < x < 10 } I
Math E-Book Release 2.2 ( )

9. O-NET / A-NET 19
B {x | x 3 } C {x | x < 5}
(13) [Ent’38] A {0, 1} B {0, {1}, {0, 1}}
(13.1) A P (B)
(13.2) {1} P (A) P (B)
(13.3) n (P (A B)) n (P (A B))
(14)
(14.1) ' U (14.7) A A'
(14.2) U' (14.8) A A' U
(14.3) A (A B) (14.9) A U U A A'
(14.4) B (A B) (14.10) A A A
(14.5) (A B) A (14.11) A A
(14.6) (A B) B (14.12) A B A B'
(15)
(15.1) A B P (A) P (B)
(15.2) A B A B
(15.3) A B A B
(15.4) A B B C B A' C' U
(15.5) A B B C A C
(16) A, B
(16.1) A B A B (16.5) x A x A B
(16.2) A B B A (16.6) x A x A' B'
(16.3) A B A B' (16.7) x A x A' B'
(16.4) (A B) ' B' A (16.8) x A x (A ' B ') '
(17)
(17.1) A (A B) (17.6) (A B) B
(17.2) (A B) B (17.7) (A B) B
(17.3) (A B) B (17.8) A (A B)
(17.4) A (A B) (17.9) (A B) (B A ')
(17.5) A (A B)
(18)
(18.1) A C B C A B
(18.2) A C B C A B
(18.3) A C B C A B
(18.4) A' B' A B
(19) A B A 3
Math E-Book Release 2.2 ( )

10. O-NET / A-NET 20
(20)
(20.1) [Ent’21] (A B) (B A) (A B)
(20.2) [A (A ' B)] [B (B ' A ')]
(20.3) [(A B) (B A)] A' A ' [(A B) (B A)]
(20.4) [(A B) ' (B C ')] [(D E) (C ' E ')] (A E ') '
(21)
(21.1) (A B C) (A ' B C) (B ' C ') U
(21.2) (A B C D ') (A ' C) (B ' C) (C D) C
(21.3) P (A B) P (A B)
(21.4) P (A B) P (B A) { }
(21.5) A B P (A B) P (A) P (B)
(22) A {0, 1, 2, 3} , B {{0}, 1, 2, {3}} C {0, {1}, {2}, 3}
(22.1) P (A) P (B) P (C ') { , {1}, {2}, {1, 2}}
(22.2) P (A) P (B ') P (C) { , {0}, {3}, {0, 3}}
(22.3) P (A ') P (B) P (C) { , {0}}
(22.4) P (A) P (B ') P (C ') { }
(23) n (U) 35 , n (A) 22 , n (B) 18
n (A ' B ')
(24) n (A) a , n (B) b , n (C) c , n (D) d
n (A B) b , n (B C) c , n (C D) d
n (A B C D) n (A B C D)
(25) A, B, C P (C) { , {a}, {c}, C} , n (P (A)) 8 , n (P (B)) 16 ,
C A , C B , {b, d, e} A B b A B'
. d (A B ') ' . e (C B ') '
. b (A ' B ') ' . {b, e} (A ' B) '
(26) A { , 1, {1}} A B'
(26.1) n [ P (A) P (B) ] 8 (26.3) P (A B) { }
(26.2) {1} P (A B) (26.4) P (B A) { }
(27) [Ent’36] A { , { }, 0, {0}, {1}, {0, 1}}
[ P (A) A] [A P (A) ]
(28) A
(28.1) A B {1, 2, 3, 4, 5} B {1, 3, 5}
(28.2) A B {1, 2, 3, ..., 15} B {2, 4, 6, 8, 10}
Math E-Book Release 2.2 ( )

11. O-NET / A-NET 21
(29) A {1, 2, 3, 4, 5, 6, 7} B {1, 2, 3}
X
(29.1) B X A
(29.2) X A B X
(30) B A n (A) 10 , n (B) 4 n (C)
(30.1) C {S |B S A}
(30.2) C {S A|S B }
(31) A {0, 2, 4, 6, 8} B {0, 1, 2} C {1, 2, 3} D {0, 2, 3}
X X A
(31.1) B C' X (31.3) B D X
(31.2) B C' X (31.4) B D X
(32) U {1, 2, 3, 4, ..., 8}
A U {1} B {2, 4, 6} C {1, 7}
D (B ' C) D A
(33) U {x I | 2 < x < 6} I
2
A {k | k U} B { k |k U}
C {x | A B x x A B}
(34) A {a, b, c, d, f} B {a, c, d, e}
X X A B A B X
(35) A {1, 3, 5, 7, 9} Sk {B A | n (B) k}
n (S) S S1 S2 S3 S4 S5
(36) A, B U n (U) 100 , n (A ') 40 , n (B) 55 ,
n (A B ') 32 n (A ' B ')
1.3
-
2 ·íÒ¤ÇÒÁe¢Ò㨴ÇÂÃÙ»ÀÒ¾¡ç´Õ¹¤Ãaº..
n (A B) n (A) n (B) n (A B) = + -
3
n (A B C) n (A) n (B) n (C) n (A B) = + +
n (A C) n (B C) n (A B C)
- - - +
Math E-Book Release 2.2 ( )

12. O-NET / A-NET 22
30
12 15 5
U
( )
U 1 “ 5 ” 5
“ 12 ” 12-5=7
“ 15 ” 15-5=10
Math Eng
30-5-7-10 = 8 ...
2 n (M) 12 , n (E) 15 , n (M E) 5 …
n (M E) n (M E) 12 15 5 22
30 22 8 ...
37 48
45 15
13 7 5
(
)
U ( )
Math Social 1 “ 5 ” 5
15-5=10,
13-5=8, 7-5=2
37-10-5-2=20,
48-10-5-8=25, 45-2-5-8=30
Thai 5+10+8+2+20+25+30 = 100
2 n (M) 37 , n (S) 48 , n (T) 45
n (M S) 15 , n (S T) 13 , n (M T) 7 n (M S T) 5 …
n (M S T) n (M S T) 37 48 45 15 13 7 5 100
( ) 100 ...
( ) (
)
Math E-Book Release 2.2 ( )

13. O-NET / A-NET 23
1.3
(37) 80 35 27
32
(38) [Ent’33] 20
( ) 17 15
(39) [Ent’34] 20
7
(40) 34
5 1
3
(41) [Ent’26] 7
, 6
5
(42) 160 100
( 30 35 ) 80
( 55 ) 50 60
(43) 35 11
16 7
23 21
(44) 600 500
300 200 50 30
25 15
(45) 3 4 4 6
,3 8 3 , 3 4 2
, 4 18 4
, , 3 4
(46) [Ent’31] 100 50 , 35
, 25 , 32 , 20 , 10
,
Math E-Book Release 2.2 ( )

14. O-NET / A-NET 24
(47) [Ent’38] 180 95
92 125 52
43 57
(48) [Ent’39] 100 U
, , 1
6 20
22 23 11
. 9
. 199
. 10
. 24
(49) 100 60 35 20
, 28 15 , 40 22 ,
14 6 , 16
10 , 20 11 ,
12 8
(50) 0 100 2 3 5
( )
(1) (1.1) (1.4) (17.1) A B (17.2) A B (29.1) 16
(2) (2.1) (2.3) (17.3) (17.4) A B (29.2) (8 1) 16
(3) (3.1) (17.5) A (17.6) A B (30.1) 64
(4) (4.3) (17.7) (17.8) A B (30.2) (16 1) 64
(5) (5.1) (5.4) (31.1) 16 (31.2) 16
(6) 9 , 126 (17.9) (31.3) 8 (31.4) 24
(7) (7.1) (7.7) (18) (18.4) (32) 16 (33) 4
(8) (8.6), (8.8), (8.10) (19) A B
(34) 56 (35) 31
A B
(9) (9.3) (36) 13 (37) 66
(10) 32, 6 (20.1) A B (20.2) B (38) 6 (39) 11
(11) . (20.3) B ' (20.4) (A E) ' (40) 13 (41) 9
(12) {1, 2, 4, 5, 6, 7, 8, 9, 10} (21) (22) (22.3) (42) 130 (43) 6
(13) , , 16-2 (23) 13 (24) d, a (25) . (44) 385
(14) (26) (26.4) (45) 26, 12, 24
(15) (15.3) (15.5) (27) 61+3 (46) 13 (47) 20
(16) (16.3),(16.4),(16.6) (28.1) 8 (28.2) 32 (48) . (49) 22-13
(50) 26
Math E-Book Release 2.2 ( )

15. O-NET / A-NET 25
( )
(1.1) x A (7.1)
x B (7.3)
A
(1.2) x (7.2) 20 1
y B, ( )
B
y A ( ) “ ( )
(1.3) {A} {B} A {B} ”
{B} B (7.4) (7.2)
(1.4) A B ( ) (7.6)
{A} {B} (7.5) P( ) (
(2.1) ( A 5 7.2)
{ } ) (7.7) { } P( ) { }
(2.2) { } A A ( 7.1)
(7.8) { } P( ) P( )
(2.3) {{a}, b} A {a} A (
b A 7.2)
(2.4) {a, b} A ( (8.1) P(A) A
) {a, b} A A ( )
a A b A (8.2) { } P(A) { } A
{a, b} A A ( A
(3.1) ( ) )
(3.2) B {A}, C {B} (8.3) P(A) !
C {{A}} ... A C
(8.4) { } P(A) P(A)
(3.3) A C (A C)
B A C (8.1)
(8.5) { , a, {b}} P(A)
A
{ , a, {b}} A
A a A {b} A
B C
(4.1) (4.2)
( ) (8.6) P(A)
(4.3) {x} A x A
(4.2) (8.7) {a} P(A) {a} A
(4.4) {x} x a A
x (8.8) {b} P(A) {b} A
b A
(5.1) 25 32 ... (5.2) (8.9) (8.8) {b} A
31 (25 1)
(5.3) P(A) 1 (8.10) { , a, {b}} P(A) P(A)
P(A) 32 ... (5.4) , a P(A) , {b} P(A)
(6) 2n 512 n 9
5 9
9!
126 ( )
5! 4!
Math E-Book Release 2.2 ( )

16. O-NET / A-NET 26
(9.1) { , {1}, {1, 2}} P(A) (13.1) A P(B) A B
{ , {1}, {1, 2}} A ( 1 B)
A {1} A {1, 2} A (13.2) P(A) P(B) P(A B)
P({0}) { , {0}}
(9.2) { , {1}, {1, 2}} P(A) ( {1} P(A) P(B) )
P(A) A (13.3) A B {0, 1, {1}, {0, 1}}
{1} P(A) {1} A 1 A n(P(A B)) 24 16
{1, 2} P(A) {1, 2} A 1 A, 2 A A B {0} n(P(A B)) 21 2
16 2 14
(9.3) {{1}, {2}, {3}} P(A) (14.1) (14.2) U
{{1}, {2}, {3}} A (complement)
{1} A, {2} A, {3} A (14.3) (14.6)
(9.4) {{1}, {2}, {3}} P(A)
{1} P(A), {2} P(A), {3} P(A) (14.7) (14.11) A A
{1} A, {2} A, {3} A (14.8) (14.10) ... (14.12) (
1 A, 2 A, 3 A !)
(10) n(X) “ (15.1) ( )
(15.2) A B
A ”
( ) A P(S) ( A S)
() 1 A 7 A ( A 1 (15.3) A B
A B A B
7)
2, 3, 4, 5, 6
(15.4) A B A B
A ...
B C B B C
{2, 3, 4, 5, 6} ..
(B C )
n(X) 25 32
A
n(Y) A A x
6 C B
A' C' (A C) ' ' U
{1} {1, 2} {1, 3} {1, 4} {1, 5} {1, 2, 3}
( A C )
A 6 .. n(Y) 6
(15.5) A B A B
(11) A B, A C, B C B C B C
A B C {3, 5} A C A C
B A C {0, 1, 2, 3, 5}
1 4 A C "A B B C
A 35 A C"
A
0 2 C
4 B A C
. A B {0}
B
C (16.1) A B
.B C {1} .. {1, 4} A B A B A B
. A C {1} (16.2) A B
.B A {2, 4} A B B A
(12) U {1, 2, 3, ..., 10} B {3, 6, 9} (16.3)
A B' A (B ') ' A B
C {1, 2, 3, 4, 5} C' B'
(16.4) B' A B' A' (B A) '
(C B) ' C B {3}
(16.5) x B
{1, 2, 4, 5, 6, 7, ..., 10}
Math E-Book Release 2.2 ( )

17. O-NET / A-NET 27
(16.6) A' B' (A B) ' (20.4) 5
x A x (A B) ' .. ( )
(16.7) x A x (A B) ' .. A' B' B C
(x B )
D E' C' E
(16.8) x A x A B ..
(x A B)
A E
(17) ( (A E)) ' (A E) '
( )
(21.1) B C
U
[(A A ') B C] (B C) '
U
A B (B C) (B C) ' U
(21.2) C
A B A B B A
C [(A B D ') A' B' D]
(17.1) A (A B) – =
A, B, D
A B
C [ (A B D ') (A B D ') ' ] C
(17.2) (A B) B = U
A B (21.3) (A B) (A B)
(17.3) (A B) B = P( ) P( )
(21.4) A B B A
(17.4) A (A B) A B P(A B) P(B A)
(17.5) A (A B) A
(17.6) (A B) B A B (21.5) A B P(A) P(B)
(17.7) (A B) B P(A) P(B) P(B) ...... (1)
(17.8) A (A B) A B A B A B B
(17.9) B A' B A P(A B) P(B) ..... (2) (1)=(2)
(A B) (B A ') (22)
(18.1) C U A B P( ) P( ) P( ) P( )
**
(18.2) C (22.1) A B C' {1, 2}
(18.3) C U (22.2) A B' C {0, 3}
(18.4) (22.3) A' B C
(19) B A B ( ) P(A ' B C) { }
A (22.4) A B' C'
(20) 2 (23) n (A ' B ') n(A B) '
(17)
n(A B) .. B A
(20.1) = = A B
n(A B) n(A) 22
(20.2) ( ) ( )
= =B n(A B) ' 35 22 13
(20.3) ( – ) ( – )= (24) n(A) a , n(B) b n(A B) b
= B' B A (B A)
D C B A
n(A B C D) n(D) d
n(A B C D) n(A) a
Math E-Book Release 2.2 ( )

18. O-NET / A-NET 28
(25) P(C) C {a, c} (33) U { 2, 1, 0, 1, 2, ..., 6}
n(P(A)) 8 n(A) 3 A {0, 1, 4} U
n(P(B)) 16 n(B) 4 B {0, 1, 2}
C A C B {0, 1} X {0, 1, 2, 4} n(C) 22 4
A {a, c, } B {a, c, , } (34) x {a, b, c, d, e, f}
{b, d, e} A B b A B' {a, c, d} X
A {a, c, b} B {a, c, d, e} X { {a,c,d} ,
. d A' B ( B A) {b,e,f} } (2 3
1)(2 ) 3
56
. e C' B (35) n(A) 5
. b A B S1 {B | B A, n(B) 1} ,
. {b, e} A B' S2 {B | B A, n(B) 2} , ...
A B' A B {b} S5 {B | B A, n(B) 5}
(26) A B ' A B A B S S1 S2 S3 S4 S5
( A B A) A (n(B)=0)
(26.1) n[P(A B)] n[P(A)] 23 8
n(S) 25 1 31
(26.2) {1} P(A B) {1} A B
(36) U
1 A B n(A B ') n(A B)
(26.3) P(A B) P( ) { } 32 32 55
(26.4) B A n(B) + 55 A B
(27) , { }, {0} n(A ' B ') n(A B) '
(26 3) (6 3) 61 3 64 n(U ) 100 ++ +
(28.1) A {2, 4, {1,3,5} } 100 32 55 13
23 8 ( .. n(A ') 40 )
(28.2) A {1, 3, 5, 7, 9, 11, 12, 13, 14, 15, (37) 35 U
{2,4,6,8,10} } 25 32 + 35
(29.1) X {1, 2, 3, {4,5,6,7} } 27
2 4
16 + 27
(29.2) X { {1,2,3} , 32 32
{4,5,6,7} } ... (2 3
1)(2 ) 4
112
+2 + + = 94
80 ( + + +)
(30.1) n(C) S 2 6
64
14
(30.2) n(C) S
+ + = 80 14 66
(24 1 6)
)(2 960
( .. n(A ' B ') n(A B) ' + +)
(31.1) {0} X {0, 2, 4, 6, 8}
(38)
24 16
(31.2) {0} X X {0, 2, 4, 6, 8}
31.1 25 24 16 20= + , 17= + , U
(31.3) {0, 2} X {0, 2, 4, 6, 8} 15= +
23 8 2( + + )=20+17+15 + + =26
(31.4) {0, 2} X X {0, 2, 4, 6, 8} 26 20 6
31.3 25 23 24
(32) {3, 5, 8} D {2, 3, 4, ..., 8}
24 16
Math E-Book Release 2.2 ( )

19. O-NET / A-NET 29
(39) U (43) + =16 ....(1)
+ + + =20 + =7 + =21-7=14 ....(2)
+ =2( + )-7
+2 + =16+14=30 24
+ + =24 11
+2 + =20 .....(1) =30-24= 6
- +2 =7 .....(2) (44) + =200
(1)x2 - (2); 3 +3 =33 + =11 U
+ =30 600
(40) +2 + =230
=15 . 500
+ + =215
600 215 385
( , U
( 43 44
) , 42)
+ + + =34 .....(1) =5 .....(2) (45)
= + +1 .....(3) + + =3 .....(4)
(2), (3) (1) (4) 4 !
+5+( +5+1)+ =34 +5+ =3 ( , 0)
=7, =9 3 4
= + +1 = 7+5+1 = 13
6, ++ 8 + 3 5 ..
(41)
2, + 4 + 18 4 14 ..
+ =7, + =6, + =5 ( + )+ + +( + )
4 2 6 14 26
U
( + )+ + 4 2 6 12
2( + + )=18 .. ++ 9
(42) 3 4
U 26 2 24
100 (46) 3 , ,
(
n(A B C) ' 100 n(A B C)
60
)
3 U
(36) 32 35
n(A B C) 20
32 35 20 87
30 + + 50 30 20 13
35 + + 60 35 25 (47) A B
55 80 55 25 n(A B C) =180 ? z
3 =95+92+125-52-43-57+x y x
+ + +2 =120 + + +2 =70 x 20 C
+ + + =100 =20 y n(A C) 20 =43-20=23
+ + =80 z n(A B) 20 =52-20=32
+ + + =60 =10
+ + =50
95 20 23 30 20
80 50 130
( ..
, )
Math E-Book Release 2.2 ( )

20. O-NET / A-NET 30
(48) (50) U {0, 1, 2, ..., 100}
x+y+20+23+22+11+9=100 x 20 y A {x|x 2 }
22 23 11 B {x|x 3 }
(x+20+23+22)=(y+20+23+11)+6 9 C {x|x 5 }
x 5, y 10
n(A ' B' C ')
70 , 64 ,
n(A B C) ' .. n(U ) n(A B C)
65
. . 70 64 65 199 n(A B C)
n(A) n(B) n(C) n(A B) n(A C))
. 5 . 5 10 9 24
n(B C) n(A B C)
(49) ( , ,
) ** 0 **
... n(A) 2 51
n(B) 3 34
n(C) 5 21
x y n(A B) 2 3 6
17 ... n(A C) 2 5
8 4
10 11 ... n(B C)
3 5 15 7
... n(A B C) 2 3 5
n(A B C) 60 8
30 4
=20+15+22-6-10-11+x ... x=22 n(A B C) 51 34 21 17 11
( ) 7 4 75
40-4 = 15+13+18-8-6-9+y ... y=13 n(U ) 101
22 13 9
n(A ' B' C ') 101 75 26
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Math E-Book Release 2.2 ( )