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不類列不了類兩列更理狀不不不了料不了列不兩裡參更更

,,,4,5,6,7, 9 數數數,,7,6 4,5 4 5 6 7 A [] a [],,,45,6,7, () () 兩兩 4 () 90 0 70 7 6 6 7 6 7 7 6 0 70 90 6 7 7 7 6 6 6 7

7 6 6 6 7 7 7 6 6 7 7 6 7 6 6 7 () 7 6 6 7 6 7 7 6 6 7 6 7 7 6 6 7 6 7 () 5 讀 P Q R P Q R P Q R 6 7 7 6 數了不 A B 不列兩兩讀列讀行行行連連讀 P Q R -P Q R -P Q R 6 讀讀 4 7 讀 4 4 讀 74 7 - 數 - 類 --Aa 不 A a 兩 --CcA 不 C c A 若論數量列

不列 4!/! 狀列 /4= 不不來數類論數量數量不兩兩,,7 A a B b 7 7 7 7 列輪 90º 不,,7,6 列 4!/! 狀列 /4= A B C 不 a b c A a B b C c 6 7 7 6 6 7 列 4

輪 90º 不,,7,6 4,5 4 列 4! 4 狀列 4/4=6 A B C D E F 不 a b c d e f A a B b C c 4 5 7 6 4 6 7 5 4 D d E e F f 5 6 7 4 7 6 5 4 6 5 7 4 7 5 6 列輪 90º 5

類不不不類若兩列例 Aa=Bb Ac=Bc A a B b A c B c 6 7 7 6 6 7 6 7 數 N N N N C C C C N 若不類度度來不類 6

例輪輪兩兩兩兩兩兩兩兩兩兩了輪不輪輪若輪類 7

類兩類類 AB ABC DEF AD ABD CEF AE ABE CDF AF ABF CDE BC ACD BEF BD ACE BDF BE ACF BDE BF ADE BCF CD ADF BCE CE AEF BCD CF DE ABCD ADEF DF ABCE ACEF EF ABCF BCDE ABDE BCDF ABDF BCEF ABEF BDEF ACDE CDEF ACDF ABCDE ACDEF ABCEF ABCDF BCDEF ABDEF AD=AE=BC= BF = CF=DE AF=BD=CE AC=CD=EF ABC=DEF=CDF=BEF ABD=ABF=ADF=BDF=BDE=BCE ACE=ACF=AEF=CEF=CDE=BCD ADE=BCF AB=BE=DF ABCE=ABCF=ADEF ACDF=CDEF ABCDE=BCDEFABCEF=ACDEF=ABDEF AB abab AaB ABbAababBAaBb 若兩 ab=ab AaB=Aab ABb=abB 若兩列論 --AB AaB=ABb

A a B A B b 6 = 7 7 6 數 i 類數 j 類數 k 類數 l 數 i i N 類數 j i-m i j i j 9 類數數 m 0 m m Z 類數 k i-n 0<k i, k< j 類數數 n 0 n m i n 0 m=n 類數 l j-k =i- m-n 0<l<i, l<j k,l k,l 若 k =l k =l k,l k,l, =, i ii-l=m-n C ( m-n ) i- m-n l- m-n =i-m C ( i-m ) 例 i j k l m n 4 4 4 0 0 4 C = AaBbCcDd 4 5 4 4 5 C 4 =0 C abbccdde abccddee AabCcDdE 5 0 5 C =0 AaBbCcDEABbCcDdEABCcDdEe 6 4 4 6 4 C /=45 C abccddef abbcddef abbccdef abbccdefabbccdefaabcddef AabCdEeF abccdef AabCcDEf AaBbcdEF AaBbcDeF AaBbcDEf 數 4 兩 ( ) 6 7 7 6 4 9

4 落若 5 4 4 A a A a A A a A A a A a A A a A A a A a a A a A A a A a a A a A A a A a A A a A A a A a A A a A A a A a a A a A A a A a a A a A A a A a A a a A a A a A A A a A a A A a A a A a A a A a A a a A a A a A 6 不 4 4 4 4 A a A a C c C c a A a A c C c C A a A a C c C c a A a A c C c C 例 5 4 4 5 4 4 4 4 4 4 B b B b B b B b B A a A a A a A a A A a B a 4 B a 4 B a B A a A a 4 B a B a B 4 A a A a 4 B a B a A 4 B 4 a B 4 a B a A a 4 B 5 4 4 4 4 5 A b A b A b A b A C c A c C c C c C A c A c C c C c C B a B 4 b B b B a B 0

5 4 4 5 A a A a A a C c C c C c A a A C c C B a B A b C 4 C a D 4 b B a c A b b 4 D a 4 B b B 4 B 4 b A 4 A b E 4 陸論裡 ( ) a a A B A B a a B B a a B B 4 a A B 4 a a A B B a a B B 4 a a B 4 b b B b A B 4 A B b B 4 b b A B 4 B b B 4 b b A B b A B A B b a b B 4 b B b b B A B b b A B b B b B A B 4 b b B 4 A B 4 b ( ) a a A B A C a a A 4 C 4 a a B 4 C A a a A C 4 a a A C 4 B C 4 a b B 4 a a A B B C a a B C A B a a B B 4 C a a A 4 B 4 B 4 C a a A 4 B 4 b A B B C b b B 4 C b b A 4 C 4 B b b B C b b B C A C b A 4 b b A B A C b b A C A B b b A A 4 C b b A 4 B 4 A 4 C b b A 4 B 4

c c A C A C c c B c c A C B 4 C c c B C A B c c A 4 B 4 A 4 C c A C c c B A B c c B C B C c c A C A B c c B 4 C c c 4 5 6 ( )

a a C a a C c B c B c c 論 0 數 45 54 若 45 5 4,,,,,,, 論,,,,,,,,,,,,,, 論,,,,,, 論 4 5 4 4 =76 論利不論數 ABb 論 4 4 4 列列類 a B A B a B a a A B --AaB a,,,,,,,,, a A ab -4-AaBb B 4 a A A a A a A a a B 4 a b A a B a A B 4 a B 4 A b A a B a

不,, a b a,, 狀列 aaaa a a b b b a bbbbaaabaabb abababbb a b a a a a b a b b b b b a b 論 a a a a 4 4 C =4 異 4 C 4 /6 4 4 異 4 C 4! /! C C 4 / 4 7 5 異 44 4+4+6+7+4=40 5 數數量 -ACc c c c c A c A -c C c -C c A c C -c C c -C c C C c A -c C c -C c C 兩 -Aa A a A a A a A a A () -Aa A C c A C c C c C c C -Cc 0 C c C - 0 -- c C C 0 C c C - 0 -- 0 A a A a A a 0 A a A () -Ab 行列 90 A b A 行列 90 b A 4 b 行列行列 A b A 0 4

() -Ab x+y=0 A b A m= 類 b A b m=- 類 90 A b A () -Ac 44 ABc c B c A --ABc--5 A c B c 4 c B -A c c A -B c 4 c B -A c c A c B c A -B c 4 c B -A c c A -B c 4 B c 4 A c c B -A c c A -B c 4 c B -A c c A -B c 4 c B -A c c A -B c 4 類類 m= m=- 例 c B c A A c B c 4 c A c B A c 4 A c B 4 c A c c 4 A 4 c B A c B 4 c c B c 4 B 4 --ABc--6 m=- m= m=- m= c 0 c 0 c 0 c m=- c 90 c 90 c 90 c m= c 90 c 90 c 90 c 90 c m=- c 0 c 0 c 0 c --ABc-4-5 A 4 c B c c A 4 c B B c B 4 c c B c 4 A 4 兩列 5

--ABc-- B c A c 4 c A c 4 B B c 4 B c c B c A 兩列 ACc B c A 4 c B c c B c A 4 c B A 4 c B c A 4 c c A B c -c B 4 c B c B 4 B c B 4 c B c B c -c B c B c 4 A 4 c B B c -c B B c -c B --ACc--. c A c 4 C C c A c 4 c C c A C c C c 兩列 c A c 4 C c 4 C C c A c 4 A c 4 c C c A c 4 C C c C c A c 4 c C c C c A C c C c C c 兩 m - AaBb 數量 4 兩 ( 例 A B) L 兩 B b A 4 0 a 4 A b 不 B b B 4 A A B B (A, A ) (A 4, A 4 ) ( A, A ) ( A 4, A 4 ) ( A 4,B 4 ) (B, B ) ( B 4, B 4 ) ( B, B ) B b A a B b A 4 a 4 A b 4 B a 4 A b B b A a B b A 4 a 4 A b 4 B a 4 A b B b A a B b B 4 A 4 a B 4 b A 4 a B b B a A b B a 4 A 4 a B 4 b A 4 a B b B a A b B a 4 A 4 a B 4 b A 4 a B 6

不 L B b A 律 a 4 A b B 4 b B 類兩兩, 類不 4 4 4 4 4 4 4 ABc A c B c A c B c A c B c A c B c A c B c A c B c A Ba 六 c B c4 A c B A c B c A c c4 A c B c4 A B c A c B c c B c4 A c B c c A c B A a B4 a B4 a B4 a B4 B a B a B a B a a 4 B a 4 B a 4 B a 4 B B a B a B a B a a B4 a B4 a B4 a B4 a B B a 4 B B a B a a a 4 B a 4 B a 4 B B a B a B a B a 兩類兩若落 7

兩 f a f 6 兩 a b A a A a A a A a A 數量數量類度不兩量更度異 () 論六兩類不 /

兩兩不 4 /4 兩兩不 7 7/6 / 7/6 /4 不兩兩兩若類兩 - 0 -- 0 - - 0 -- 0 - -Bb 0 90 90 0 0 90 90 0 B b 4 B b B b 4 B b 4 B b 4 B b 4 B b B b B b B 4 b B b B b B b 4 B b 4 B b 4 -Ab x+y=0 m= 類 m=- 類 90 4 -Ac 例 ABc c B -A c c A -B c 4 c B -A c c A -B c 4 c B -A c c A -B c 4 c B -A c c A -B c 4 c B -A c c A -B c 4 c B -A c c A -B c 4 類 m= m=- 率 m= m=- 若 m= m=- 9

m= c 0 c 0 c 0 c m=- c 90 c 90 c 90 c 90 c 4 m= c 90 c 90 c 90 c 90 c m=- c 0 c 0 c 0 c 4 兩兩落數兩度異兩類 90 70 不不了 / 兩兩 6 4 不 /4 兩兩 6 7 不 7/6 4 兩若類數量數量良列列類論,,,, 利列數量來六六參料數 6 / 9 年 9 http://www.csjh.tc.edu.tw 0