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Set Set Document Transcript

  • O-NET / A-NET 11 {s,e,t} º··Õè 1 e«µ “ ” (Set) , 7, 360 , (Element Member) A, B, C { } A , B 7, C 360 , D 7, E 3 33A { , , , , , , } (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 ( )
  • O-NET / A-NET 12 (Finite S ¨u´·Õè¼i´ºoÂ! SSet) “ A” n (A) e«µµo仹ÕÁÕ¨íҹǹÊÁÒªi¡e·Òã´ é 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}G 0 1 (¤Ùoa¹´aº 1-2 ¡aº 2-1 ¶×oÇÒµÒ§¡a¹ æµe«µ 1-2 ¡aºe«µ 2-1 ¶×oÇÒeËÁ×o¹¡a¹æÅäÁ F {1, 0, 1, 2, 3, ...} , n (F) µo§¹aº«éíÒ¹¤Ãaº) G { | } e«µ¢o§ª×èo¤¹ã¹»Ãe·Èä·Âã¹¢³¹ÕéG {x |0 x 1} e»¹e«µ¨íÒ¡a´ËÃ×oo¹a¹µ ... ¤íÒµoº¤×o e«µ¨íÒ¡a´¤Ãaº ¶Ö§æÁ¨íҹǹÊÁÒªi¡¨´ÙÇÒ x( ) 0 x 1 ( ) 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 ( )
  • O-NET / A-NET 131. A2. A A3. 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 ( )
  • 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 B2, 4, 6 Y ( 1, 3, 5, 7Y 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 ( )
  • 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 ( )
  • 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 C1. (Union : ) ... A B A B U U U A A B A B B A B B2. (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 A4. (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 ( )
  • 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 ( )
  • 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 ... CP (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 BU {x I | 1 < x < 10 } I Math E-Book Release 2.2 ( )
  • O-NET / A-NET 19B {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 ( )
  • 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) dn (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 ( )
  • 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 2A {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) = + - 3n (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 ( )
  • 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) 45n (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 ( )
  • 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 ( )
  • 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 ( )
  • 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, ( ) By 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 ( )
  • 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 BA ”( ) 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 CA 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 BC {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 ( )
  • 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, DA 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 ( )
  • 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} Un(P(B)) 16 n(B) 4 B {0, 1, 2} C A C B {0, 1} X {0, 1, 2, 4} n(C) 22 4A {a, c, } B {a, c, , } (34) x {a, b, c, d, e, f} {b, d, e} A B b A B {a, c, d} XA {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) U1 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 1323 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} } 272 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 ( )
  • 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 6 122( + + )=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 8730 + + 50 30 20 1335 + + 60 35 25 (47) A B55 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 ( )
  • 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 7540-4 = 15+13+18-8-6-9+y ... y=13 n(U ) 101 22 13 9 n(A B C ) 101 75 26 S ¨u´·Õè¼i´ºoÂ! S ¨Ò¡¢o (50) ËÒ¡¨·Âe»ÅÕè¹ä»e»¹ A ¤×oe«µ¢o§¨íҹǹ·ÕèËÒà 6 ŧµaÇ æÅ B ¤×oe«µ¢o§¨íҹǹ·ÕèËÒà 8 ŧµaÇ æÅÇ A B ¨e»¹e«µ¢o§¨íҹǹ溺㴤Ãaº.. ËÅÒ¤¹µoºÇÒ ËÒ÷aé§ 6 æÅ 8 ŧµaÇ ¡çæ»ÅÇÒËÒà 48 ŧµaÇ ... äÁ㪹¤Ãaº! ... eoÒ 6 ¡aº 8 ÁÒ¤Ù³¡a¹¹aé¹¼i´! ¨µo§ãª ¤.Ã.¹. ¤×o ËÒà 24 ŧµaÇ ¨Ö§¨¶Ù¡ Math E-Book Release 2.2 ( )