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2. O-NET / A-NET 12
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Math E-Book Release 2.2 ( )
3. O-NET / A-NET 13
1. A
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Math E-Book Release 2.2 ( )
4. O-NET / A-NET 14
E { , {0}, { }} P(E)
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(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} }
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(5.1) n (A) 5 A 32
(5.2) n (A) 5 A 32
(5.3) n (A) 5 A 32
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(7.2) (7.6) P( )
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(7.4) { } (7.8) { } P( )
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(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)
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(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}
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Math E-Book Release 2.2 ( )
6. O-NET / A-NET 16
U U U
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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
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B A “ B A”
U U U
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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)
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Math E-Book Release 2.2 ( )
8. O-NET / A-NET 18
C { , { }, 0, {{ }, 0}, { , {0}}, {{ , {0}}}}
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n (C) 6 n (P (C)) 26 64
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(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'
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(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}
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D (B ' C) D A
(33) U {x I | 2 < x < 6} I
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A {k | k U} B { k |k U}
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(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 ,
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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
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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
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45 15
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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 ( )
15. O-NET / A-NET 25
( )
(1.1) x A (7.1)
x B (7.3)
A
(1.2) x (7.2) 20 1
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31 (25 1)
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P(A) 32 ... (5.4) , a P(A) , {b} P(A)
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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)
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P(A) A (13.3) A B {0, 1, {1}, {0, 1}}
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(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 ( )
