北京大学：离散数学（一）：27.3

27 x3 a0 N L a1 a2 a3 a4 a5 a6 a7 a8 a9 a10 a7 a11 a12 a7 a13 a14 a15 a16a17 a18 L a19 : a20 8 > > > > > > > > > > > > > > > > > > > > < > > > > > > > > > > > > > > > > > > > > : a20 8 > > > > > < > > > > > : a21a22 1 N L L, N L : : { L a19 : { : ? { : 15 (1){(10) N 2 ‘ ; ‘ (+) : a23 (+) a24 a25 a26 a27 3 8 ‘ 8x , t x a21a22 a28 ‘ (x=t) (8 ) a20 x, (x) a29 , a30 x" " t a29 a31 : "t x a21a22 " a32 4 8 ‘ , x a21a22 ‘ 8x (8+) a20 (x) (x) a29 , x , x, (x) a29 a31 : a33a34 "x a35 a36 a37 a38a39 a40 a41a42 a43a44 a45 a46 " a35a47 a48 . 5 9 ; ‘ , x [f g a21a22 ; 9x ‘ (9 ) a20 (x) a49 (x) a29 , x 9x (x) (x) a29 a31 : " " "9x " a50 : a33a34 "x a35 a36 [f g a37 a38a39 a40 a41a42 a43a44 a45 a46 " a35a47 a48 . 6 9 ‘ (x=t), t x a21a22 a28 ‘ 9x (9+) a20 a30 x" " t a29 , a49 a49 x a29 . (t 9x a29 " ".) : "t x a21a22 " a32 7 : (x=x) = , x x a21a22 . ‘ 8x , ‘ ((8 ) t x) ‘ , ‘ (9x) ((9+) t x) 8 N L 1 ‘ 1 ; 2 ‘ 2 ; ; n ‘ n : (1) i (i : 1 i n) N L a32 (2) i ‘ i (1 i n) j ‘ j (1 j < i) N L . N L a19 ( ) a51 . n a22 n N L , n ‘ N L n , n ‘ n . a52 a53 a54 N a42 a55 a56 a57a58 a37 a59a60 a61a62 a63 a64 a65 9 N N L 1 N , [f g p 0 ; p 1 ; ; p n , 0 ; 1 ; ; n L , 0 ; 1 ; ; n [f g p 0 ; p 1 ; ; p n , L 0 0 a66 ‘ N , 0 ‘ N L 0 . 10 1 : ‘ N , N : 1 ‘ 1 ; 2 ‘ 2 ; ; k ‘ k (= ‘ ) 1 [ [ k [f 1 ; 2 ; ; k g p 0 ; ; p n ; p n+1 ; ; p n+m . L m n+1 ; ; n+m , 1 ; 2 ; ; k ; 1 ; 2 ; ; k p 0 ; ; p n ; p n+1 ; ; p n+m 0 ; ; n ; n+1 ; ; n+m 0 1 ; 0 2 ; ; 0 k ; 0 1 ; 0 2 ; ; 0 k . 11 1 ( ) 0 1 ‘ 0 1 ; 0 2 ‘ 0 2 ; ; 0 k ‘ 0 K N L a19 . ( N N L . .) 0 k = 0 , 0 k = 0 , 0 ‘ N L 0 . 12 a67a67a67 2 L 1 ; 2 ; ; n . 1. ‘ N L 1 ; 2 ; ; n , 1 ; 2 ; ; n ‘ N L , ‘ N L . 2. 1 ! 2 ‘ N L 3 ! 4 , 1 ‘ N L 2 , 3 ‘ N L 4 . a19 a32 13 6 N L : 1. 8x( ! ) ‘a !8x , x a21a22 . 2. 8x( ! ) ‘a 9x ! , x a21a22 . 3. 8x( ! ) ‘ 9x !9x , 4. 8x( ! ) ‘ 8x !8x , 14 6(1)(‘) 1. 8x( ! ) ‘a !8x , x a21a22 . : (‘) (1) 8x( ! ); ‘ 8x( ! ) (2) (2) 8x( ! ); ‘ ! (8 ) (3) 8x( ! ); ‘ (2) (4) 8x( ! ); ‘ (! ) (5) 8x( ! ); ‘ 8x (x a21a22 ) (8+) (6) 8x( ! ) ‘ !8x (! +) 15 6(1)(a) 1. 8x( ! ) ‘a !8x , x a21a22 . : (a) (1) !8x ; ‘ !8x (2) (2) !8x ; ‘ (2) (3) !8x ; ‘ 8x (! ) (4) !8x ; ‘ (8 ) (5) !8x ‘ ! (! +) (6) !8x ‘ 8x( ! ) (x a21a22 ) (8+) 16 6(2)(‘) 2. 8x( ! ) ‘a 9x ! , x a21a22 . : (a) (1) 8x( ! ); ‘ 8x( ! ) (2) (2) 8x( ! ); ‘ ! (8 ) (3) 8x( ! ); ‘ (2) (4) 8x( ! ); ‘ (! ) (5) 8x( ! ); 9x ‘ (x 8x( ! ) a21a22 ) (9 ) (6) 8x( ! ) ‘ 9x ! (! +) 17 6(1)(a) 2. 8x( ! ) ‘a 9x ! , x a21a22 . : (a) (1) 9x ! ; ‘ (2) (2) 9x ! ; ‘ 9x (9+) (3) 9x ! ; ‘ 9x ! (2) (4) 9x ! ; ‘ (! ) (5) 9x ! ‘ ! (! +) (6) 9x ! ‘ 8x( ! ) (x a21a22 ) (8+) 18 6(3) 3. 8x( ! ) ‘ 9x !9x : (1) 8x( ! ); ‘ 8x( ! ) (2) (2) 8x( ! ); ‘ ! (8 ) (3) 8x( ! ); ‘ (2) (4) 8x( ! ); ‘ (! ) (5) 8x( ! ); ‘ 9x (9+) (6) 8x( ! ); 9x ‘ 9x (9 ) (7) 8x( ! ) ‘ 9x !9x (! +) 19 6(4) 4. 8x( ! ) ‘ 8x !8x : (1) 8x( ! ); 8x ‘ 8x( ! ) (2) (2) 8x( ! ); 8x ‘ ! (8 ) (3) 8x( ! ); 8x ‘ 8 (2) (4) 8x( ! ); 8x ‘ (8 ) (5) 8x( ! ); 8x ‘ (! ) (6) 8x( ! ); 8x ‘ 8x (8+) (7) 8x( ! ) ‘ 8x !8x (! +) 20 p.559(p.184) 14. (2),(4),(5) 21 22 N L N : : N L N 8 > < > : + : N L N 8 > > > > > < > > > > > : ( ) ( N ) ( a21a22 ) a20 N L N (8+), (8 ), (9+), (9 ) a20 a19 N a68 a69 a70 a71a72 "a73 a74 "N L a68 a69 a70 a71a72 (a75 a76a77 a78 a79 a68 a80 a81 a74a83a82 a84 a68 .) N L a85 a86 a87 a88 a87a89 a90 a91 a92 a93 . : N N L a29 a27 23 7 y x a21a22 , y a21a22 , 1.9x ‘a 9y (x=y): 2.8x ‘a 8y (x=y): : y x a21a22 , y a21a22 , (x=y)(y=x) = . a21a22 # # # : ( x x y ) (x=y) : ( y x y ) (x=y)(y=x) : ( x x y ) 24 7 y x a21a22 , y a21a22 , 1.9x ‘a 9y (x=y): 2.8x ‘a 8y (x=y): : 1. (‘) (1) ‘ (2) (2) ‘ (x=y)(y=x) (3) ‘ 9y (x=y) (x y (x=y) a21a22 ) (9+) (4) 9x ‘ 9y (x=y) (x 9y (x=y) a21a22 ) (9 ) 25 7 ( ) y x a21a22 , y a21a22 , 1.9x ‘a 9y (x=y): 2.8x ‘a 8y (x=y): : 1. (a) (1) 9y (x=y) ‘ 9x (x=y)(y=x) (‘) (2) 9y (x=y) ‘ 9x a20 a49 a26 a29 , a27 26 8 : 8xy ‘ 8yx : (1) 8xy ‘ 8xy (2) (2) 8xy ‘ 8y (8 ) (3) 8y ‘ (8 ) (4) 8xy ‘ (Tr) (5) 8xy ‘ 8x (8+) (6) 8xy ‘ 8y8x (8+) 27 9 : 1. 8x ‘a :9x: 2. 9x ‘a :8x: : 1. (a) (1) : ‘ : (2) (2) : ‘ 9x: (9+) (3) : !9x: ‘ :9x: ! ( 1) (4) :9x: ‘ ( 2(2)) (5) :9x: ‘ 8x (8+) 28 9( ) : 1. 8x ‘a :9x: 2. 9x ‘a :8x: : 1(‘). (‘) (1) 8x ‘ 8x (2) (2) 8x ‘ (8 ) (3) : ‘ :8x ( 2(2)) (4) 9x: ‘ :8x (9 ) (5) 8x ‘ :9x: ( 2(2)) 29 10 : 1. 9x( ! ) ‘a !9x x a21a22 . 2. 9x( ! ) ‘a 8x ! x a21a22 . 30 10(1)(‘) 1.9x( ! ) ‘a !9x x a21a22 . : (‘) (1) ! ; ‘ (2) (2) ! ; ‘ ! (2) (3) ! ; ‘ (! ) (4) ! ; ‘ 9x (9+) (5) ! ‘ !9x (! +) (6) 9x( ! ) ‘ !9x (x !9x a21a22 ) (9 ) 31 10(1)(a) 1.9x( ! ) ‘a !9x x a21a22 . : (a) (1) :8x:( ! ) ‘ 9x( ! ) ( 9) (2) :9x( ! ) ‘ 8x:( ! ) ( 2) (3) :9x( ! ) ‘ :( ! ) (8 )(2) (4) ‘ ! ( 1) (5) :( ! ) ‘ : ( 2) (6) : ‘ ! ( 1) (7) :( ! ) ‘ ( 2) (8) :9x( ! ) ‘ : ; (Tr)(3;5;7) (9) :9x( ! ) ‘ 8x: (8+)(8) 32 10(1)(a) ( 1) 1.9x( ! ) ‘a !9x x a21a22 . : (10) ! 9x ;:9x( ! ) ‘ (+)(8) (11) ! 9x ;:9x( ! ) ‘ ! 9x (2) (12) ! 9x ;:9x( ! ) ‘ 9x (! )(10,11) (13) ! 9x ;:9x( ! ) ‘ 8x: (+)(9) (14) 9x ‘ :8x: ( 9) (15) 8x: ‘ :9x ( 2) (16) ! 9x ;:9x( ! ) ‘ :9x (Tr)(13,15) (17) ! 9x ‘ 9x( ! ) (: )(12,16) 33 10(1)(a) ( 2) 1.9x( ! ) ‘a !9x x a21a22 . a94 : (10) 9x ‘ :8x: ( 9) (11) 8x: ‘ :9x ( 2) (12) :9x( ! ) ‘ :9x (Tr)(9;11) (13) :9x( ! ) ‘ ^:9x (^+)(8;12) (14) ^:9x ‘ :( ! 9x ) ( 1) (15) :9x( ! ) ‘ :( ! 9x ) (Tr)(13;14) (16) ! 9x ‘ 9x( ! ) ( 2) a20 "xa26 a95 a96 a97 " 34 10(2)(‘) 2. 9x( ! ) ‘a 8x ! x a21a22 . : (‘) (1) ! ; 8x ‘ 8x (2) (2) ! ; 8x ‘ (8 ) (3) ! ; 8x ‘ ! (2) (4) ! ; 8x ‘ (! ) (5) ! ‘ 8x ! (! +) (6) 9x( ! ) ‘ 8x ! (x 8x ! a21a22 ) (9 ) 35 10(2)(a) 2. 9x( ! ) ‘a 8x ! x a21a22 . : (a) (1) 8x:( ! ) ‘ 8x:( ! ) (2) (2) 8x:( ! ) ‘ :( ! ) (8 )(1) (3) :( ! ) ‘ ^: ( 1) (4) ^: ‘ ; : ( 1) (5) 8x:( ! ) ‘ ; : (Tr)(2;3;4) (6) 8x:( ! ) ‘ 8x (8+)(5) (7) 8x ; : ‘ 8x ^: ( 1) 36 10(2)(a) ( ) 1.9x( ! ) ‘a !9x x a21a22 . : (8) 8x ^: ‘ :(8x ! ) ( 1) (9) 8x:( ! ) ‘ :(8x ! ) (Tr)(5,6,7,8) (10) 8x ! ‘ :8x:( ! ) ( 2) (11) :8x:( ! ) ‘ 9x( ! ) ( 9) (12) 8x ! ‘ 9x( ! ) (Tr)(10;11) a20 "xa26 a95 a96 a97 " 37 11 : 1: 8x( $ ) ‘ 8x $8x 2: 8x( $ ) ‘ 9x $ 9x 38 11(1) 1. 8x( $ ) ‘ 8x $8x : (1) 8x( $ ); 8x ‘ 8x( $ ) (2) (2) 8x( $ ); 8x ‘ $ (8 )(11) (3) 8x( $ ); 8x ‘ 8x (2) (4) 8x( $ ); 8x ‘ (8 )(3) (5) 8x( $ ); 8x ‘ ($ )(2;4) (6) 8x( $ ); 8x ‘ 8x (8+)(5) (7) 8x( $ ); 8x ‘ 8x ( (6)) (8) 8x( $ ) ‘ 8x $ 8x ($ +)(6;7) 39 11(1) 2. 8x( $ ) ‘ 9x $ 9x : (1) 8x( $ ); ‘ 8x( $ ) (2) (2) 8x( $ ); ‘ $ (8 )(1) (3) 8x( $ ); ‘ (2) (4) 8x( $ ); ‘ ($ )(2;3) (5) 8x( $ ); ‘ 9x (9+)(4) (6) 8x( $ ); 9x ‘ 9x (9 )(5) (7) 8x( $ ); 9x ‘ 9x ( (6)) (8) 8x( $ ) ‘ 9x $ 9x ($ +)(6;7) 40 12 : x a21a22 , 1: ^8x ‘a 8x( ^ ) 2: ^9x ‘a 9x( ^ ) 3: _8x ‘a 8x( _ ) 4: _9x ‘a 9x( _ ) 1 3. 41 12(1)(‘) 1. ^8x ‘a 8x( ^ ), x a21a22 . : (‘) (1) ^8x ‘ ^8x (2) (2) ^8x ‘ (^ )(1) (3) ^8x ‘ 8x (^ )(1) (4) ^8x ‘ (8 )(3) (5) ^8x ‘ ^ (^+)(2;4) (6) ^8x ‘ 8x( ^ ) (x ^8x a21a22 ) (8+)(5) 42 12(1)(a) 1. ^8x ‘a 8x( ^ ), x a21a22 . : (a) (1) 8x( ^ ) ‘ 8x( ^ ) (2) (2) 8x( ^ ) ‘ ^ (8 )(1) (3) 8x( ^ ) ‘ (^ )(2) (4) 8x( ^ ) ‘ (^ )(2) (5) 8x( ^ ) ‘ 8x (8+)(4) (6) 8x( ^ ) ‘ ^8x (^+)(3;5) : "x a26 a95 a96 a97 ". 43 12(3)(‘) 3. _8x ‘a 8x( _ ), x a21a22 . : (‘) (1) ‘ (2) (2) ‘ _ (_+)(1) (3) ‘ 8x( _ ) (x a21a22 ) (8+)(2) (4) 8x ‘ 8x (2) (5) 8x ‘ (8 )(4) (6) 8x ‘ _ (_+)(5) (7) 8x ‘ 8x( _ ) (8+)(6) (8) _8x ‘ 8x( _ ) (_ )(3;6) 44 12(3)(a) 3. _8x ‘a 8x( _ ), x a21a22 . : (a) (1) 8x( _ );: ‘ 8x( _ ) (2) (2) 8x( _ );: ‘ _ (8 )(1) (3) _ ‘ : ! ( a98 ) (4) 8x( _ );: ‘ : ! (Tr)(2;3) (5) 8x( _ );: ‘ : (2) (6) 8x( _ );: ‘ (! )(4;5) (7) 8x( _ );: ‘ 8x (8+)(6) (8) 8x( _ ) ‘ : ! 8x (! +)(7) (9) : ! 8x ‘ _8x ( a98 ) (10) 8x( _ ) ‘ _8x (Tr)(8;9) 45 p.559(p.184) 6. y x a21a22 , y a26 a95 a96 a97 , 8x ‘a 8y (x=y): 7. 9. 12 (2),(4) 12. a20 ; ‘ N L , x a26 a95 a96 a97 , ;9x ‘ N L 9x . 13. a20 ; ‘ N L , x [f g a21a22 , ;9x ‘ N L 8x . 14. (2),(4),(5) 46 47 N L a19 : 8 > < > : ! 8x ‘a 8x( ! ) ! 9x ‘a 9x( ! ) x a21a22 8 > < > : 8x ! ‘a 9x( ! ) 9x ! ‘a 8x( ! ) x a21a22 8 > > > > > > > > > < > > > > > > > > > : ^8x ‘a 8x( ^ ) ^9x ‘a 9x( ^ ) _8x ‘a 8x( _ ) _9x ‘a 9x( _ ) x a21a22 48 ( ) N L a19 : 8 > < > : :8x ‘a 9x: :9x ‘a 8x: 8 > < > : 8x ‘a 8y (x=y) 9x ‘a 8y (x=y) y a20 8x( $ ) ‘ 8x $ 8x ? 8x( $ ) ‘ 9x $ 9x ? 9x( $ ) ‘ 9x $ 9x ? 9x( $ ) ‘ 8x $ 8x ? 49 3 ; ; L , ‘a . 0 . ‘a 0 . : : # # # 0 : 50 1 L ; 0 ; ; 0 ‘a 0 , ‘a 0 , : 1. : ‘a : 0 2. _ ‘a 0 _ 0 3. ^ ‘a 0 ^ 0 4. ! ‘a 0 ! 0 5. $ ‘a 0 $ 0 6. 8x ‘a 8x 0 7. 9x ‘a 9x 0 (7). 51 1(7) L ; 0 ; ; 0 ‘a 0 , ‘a 0 , : 7. 9x ‘a 9x 0 : (1) ‘a 0 (2) ; ‘ $ 0 (3) ; ‘ 8x( $ 0 ) (4) 8x( $ 0 ) ‘ 9x $9x 0 ( 11) (5) ; ‘ 9x $9x 0 (Tr) (6) 9x ‘ 9x $9x 0 (+) (7) 9x ‘ 9x (8) 9x ‘ 9x 0 (9) 9x 0 ‘ 9x ( (8)) (10) 9x ‘a 9x 0 52 1(7) ( ) L ; 0 ; ; 0 ‘a 0 , ‘a 0 , : 7. 9x ‘a 9x 0 a94 : (1) ‘ 0 ( a99 ) (2) ‘ 9x 0 (9+)(1) (3) 9x ‘ 9x 0 (9 )(2) (4) 9x 0 ‘ 9x ( (3)) (5) 9x ‘a 9x 0 53 3 ; ; L , ‘a . 0 . ‘a 0 . : d a66 (1) d = 0 , , : = 0 , = 0 = , ‘a 0 . (2) d n . d = n + 1 a66 a19 : : 1 , 1 _ 2 , 1 ^ 2 , 1 ! 2 , 1 $ 2 , 9x 1 , 8x 1 . , 1 2 n 54 ( ) 1 2 0 1 0 2 . a22 : 1 ‘a 0 2 , 2 ‘a 9 0 2 . 0 : : 0 1 , 0 1 _ 0 2 , 0 1 ^ 0 2 , 0 1 ! 0 2 , 0 1 $ 0 2 , 9x 0 1 , 8x 0 1 . 1 ‘a 0 . a66 55 a67a67a67 12(1) : x a21a22 , : 8x( ^ ) ‘a ^8x : (1) ^ ‘a :( !: ) ( a98 ) (2)8x( ^ ) ‘a 8x:( !: ) (3):8x( ^ ) ‘a :8x:( !: ) ( 2) (4):8x:( !: ) ‘a 9x( !: ) ( 9) (5)9x( !: ) ‘a !9x: ( 10) (6):8x( ^ ) ‘a !9x: (Tr) (7)8x( ^ ) ‘a :( !9x: ) ( 2) (8):( !9x: ) ‘a ^:9x: ( a98 ) (9)8x( ^ ) ‘a ^:9x: (Tr) (10)8x( ^ ) ‘a ^8x ( ) 56 10 L a19 : Q 1 v 1 Q 2 v 2 Q n v n : Q i 8 9 (1 i n); v i (1 i n); n a21 (n = 0); . L a19 . 57 ( ) 4 L a19 , L a19 0 , ‘a 0 . 0 a19 . a100 a101 a51 . 58 8 . 1. : 8x 2 9x 1 F 2 1 (x 1 ; x 2 ) 2. 8x 1 F 1 (x 1 )!8x 2 F 1 (x 2 ) 3. 8x 1 F 2 1 (x 1 ; x 2 )!8x 2 F 1 (x 2 ) 4. 8x 1 F 2 1 (x 1 ; x 2 )!:9x 2 F 1 2 (x 2 ) ! 8x 1 8x 2 F 2 3 (x 1 ; x 2 ) 5. 8x 1 F 2 1 (x 1 ; x 2 ) $ 8x 2 F 2 1 (x 1 ; x 2 ) 59 8(1) 1. : 8x 2 9x 1 F 2 1 (x 1 ; x 2 ) : : 8x 2 9x 1 F 2 1 (x 1 ; x 2 ) ‘a 9x 2 :9x 1 F 2 1 (x 1 ; x 2 ) ‘a 9x 2 8x 1 (:F 2 1 (x 1 ; x 2 )) 60 8(2) 2. 8x 1 F 1 (x 1 )!8x 2 F 1 (x 2 ) : 8x 1 F 1 (x 1 )!8x 2 F 1 (x 2 ) ‘a 8x 2 8x 1 F 1 (x 1 )!F 1 (x 2 ) ‘a 8x 2 9x 1 F 1 (x 1 )!F 1 (x 2 ) 61 8(2) 2. 8x 1 F 1 (x 1 )!8x 2 F 1 (x 2 ) : 8x 1 F 1 (x 1 )!8x 2 F 1 (x 2 ) ‘a 8x 2 8x 1 F 1 (x 1 )!F 1 (x 2 ) ‘a 8x 2 9x 1 F 1 (x 1 )!F 1 (x 2 ) a94 : 8x 1 F 1 (x 1 )!8x 2 F 1 (x 2 ) ‘a 9x 1 F 1 (x 1 )!8x 2 F 1 (x 2 ) ‘a 9x 1 8x 2 F 1 (x 1 )!F 1 (x 2 ) : a26 a49 a49 61-a 8(3) 3. 8x 1 F 2 1 (x 1 ; x 2 )!8x 2 F 1 (x 2 ) : 8x 1 F 2 1 (x 1 ; x 2 )!8x 2 F 1 (x 2 ) ‘a 8x 2 8x 1 F 2 1 (x 1 ; x 2 )!F 1 (x 2 ) ‘a 8x 2 9x 1 F 2 1 (x 1 ; x 2 )!F 1 (x 2 ) 62 8(3) 3. 8x 1 F 2 1 (x 1 ; x 2 )!8x 2 F 1 (x 2 ) : 8x 1 F 2 1 (x 1 ; x 2 )!8x 2 F 1 (x 2 ) ‘a 8x 2 8x 1 F 2 1 (x 1 ; x 2 )!F 1 (x 2 ) ‘a 8x 2 9x 1 F 2 1 (x 1 ; x 2 )!F 1 (x 2 ) 62-a 8(3) 3. 8x 1 F 2 1 (x 1 ; x 2 )!8x 2 F 1 (x 2 ) : 8x 1 F 2 1 (x 1 ; x 2 )!8x 2 F 1 (x 2 ) ‘a 8x 2 8x 1 F 2 1 (x 1 ; x 2 )!F 1 (x 2 ) ‘a 8x 2 9x 1 F 2 1 (x 1 ; x 2 )!F 1 (x 2 ) : 8x 1 F 2 1 (x 1 ; x 2 )!8x 2 F 1 (x 2 ) ‘a 8x 1 F 2 1 (x 1 ; x 3 )!8x 2 F 1 (x 2 ) ‘a 8x 2 8x 1 F 2 1 (x 1 ; x 3 )!F 1 (x 2 ) ‘a 8x 2 9x 1 F 2 1 (x 1 ; x 3 )!F 1 (x 2 ) 62-b 8(3) 3. 8x 1 F 2 1 (x 1 ; x 2 )!8x 2 F 1 (x 2 ) : 8x 1 F 2 1 (x 1 ; x 2 )!8x 2 F 1 (x 2 ) ‘a 8x 2 8x 1 F 2 1 (x 1 ; x 2 )!F 1 (x 2 ) ‘a 8x 2 9x 1 F 2 1 (x 1 ; x 2 )!F 1 (x 2 ) : 8x 1 F 2 1 (x 1 ; x 2 )!8x 2 F 1 (x 2 ) ‘a 8x 1 F 2 1 (x 1 ; x 3 )!8x 2 F 1 (x 2 ) ‘a 8x 2 8x 1 F 2 1 (x 1 ; x 3 )!F 1 (x 2 ) ‘a 8x 2 9x 1 F 2 1 (x 1 ; x 3 )!F 1 (x 2 ) 62-c 8(3) 3. 8x 1 F 2 1 (x 1 ; x 2 )!8x 2 F 1 (x 2 ) : 8x 1 F 2 1 (x 1 ; x 2 )!8x 2 F 1 (x 2 ) ‘a 8x 1 F 2 1 (x 1 ; x 2 )!8x 3 F 1 (x 3 ) ‘a 8x 3 8x 1 F 2 1 (x 1 ; x 2 )!F 1 (x 3 ) ‘a 8x 3 9x 1 F 2 1 (x 1 ; x 2 )!F 1 (x 3 ) 63 8(3) 3. 8x 1 F 2 1 (x 1 ; x 2 )!8x 2 F 1 (x 2 ) : 8x 1 F 2 1 (x 1 ; x 2 )!8x 2 F 1 (x 2 ) ‘a 8x 1 F 2 1 (x 1 ; x 2 )!8x 3 F 1 (x 3 ) ‘a 8x 3 8x 1 F 2 1 (x 1 ; x 2 )!F 1 (x 3 ) ‘a 8x 3 9x 1 F 2 1 (x 1 ; x 2 )!F 1 (x 3 ) a94 : 8x 1 F 2 1 (x 1 ; x 2 )!8x 2 F 1 (x 2 ) ‘a 9x 1 (F 2 1 (x 1 ; x 2 )!8x 2 F 1 (x 2 )) ‘a 9x 1 (F 2 1 (x 1 ; x 2 )!8x 3 F 1 (x 3 )) ‘a 9x 1 8x 3 (F 2 1 (x 1 ; x 2 )!F 1 (x 3 )) 63-a 8(4) 4. 8x 1 F 2 1 (x 1 ; x 2 )!:9x 2 F 1 2 (x 2 ) !8x 1 8x 2 F 2 3 (x 1 ; x 2 ) a102 : 8x 1 F 2 1 (x 1 ; x 2 )!:9x 2 F 1 2 (x 2 ) !8x 1 8x 2 F 2 3 (x 1 ; x 2 ) ‘a 8x 1 F 2 1 (x 1 ; x 2 )!8x 2 :F 1 2 (x 2 ) !8x 1 8x 2 F 2 3 (x 1 ; x 2 ) ‘a 9x 1 F 2 1 (x 1 ; x 2 )!8x 2 :F 1 2 (x 2 ) !8x 1 8x 2 F 2 3 (x 1 ; x 2 ) ‘a 9x 1 F 2 1 (x 1 ; x 2 )!8x 3 :F 1 2 (x 3 ) !8x 1 8x 2 F 2 3 (x 1 ; x 2 ) ‘a 9x 1 8x 3 F 2 1 (x 1 ; x 2 )!:F 1 2 (x 3 ) !8x 1 8x 2 F 2 3 (x 1 ; x 2 ) ‘a 9x 1 8x 3 F 2 1 (x 1 ; x 2 )!:F 1 2 (x 3 ) !8x 4 8x 5 F 2 3 (x 4 ; x 5 ) ‘a 8x 1 9x 3 F 2 1 (x 1 ; x 2 )!:F 1 2 (x 3 ) !8x 4 8x 5 F 2 3 (x 4 ; x 5 ) ‘a 8x 1 9x 3 8x 4 8x 5 F 2 1 (x 1 ; x 2 )!:F 1 2 (x 3 ) !F 2 3 (x 4 ; x 5 ) 64 8(5) 5. 8x 1 F 2 1 (x 1 ; x 2 ) $ 8x 2 F 2 1 (x 1 ; x 2 ) : 8x 1 F 2 1 (x 1 ; x 2 ) $ 8x 2 F 2 1 (x 1 ; x 2 ) ‘a 8x 1 F 2 1 (x 1 ; x 2 ) ! 8x 2 F 2 1 (x 1 ; x 2 ) V 8x 2 F 2 1 (x 1 ; x 2 ) ! 8x 1 F 2 1 (x 1 ; x 2 ) ‘a 8x 3 F 2 1 (x 3 ; x 2 ) ! 8x 4 F 2 1 (x 1 ; x 4 ) V 8x 5 F 2 1 (x 1 ; x 5 ) ! 8x 6 F 2 1 (x 6 ; x 2 ) ‘a 9x 3 F 2 1 (x 3 ; x 2 ) ! 8x 4 F 2 1 (x 1 ; x 4 ) V 9x 5 F 2 1 (x 1 ; x 5 ) ! 8x 6 F 2 1 (x 6 ; x 2 ) ‘a 9x 3 8x 4 F 2 1 (x 3 ; x 2 ) ! F 2 1 (x 1 ; x 4 ) V 9x 5 8x 6 F 2 1 (x 1 ; x 5 ) ! F 2 1 (x 6 ; x 2 ) ‘a 9x 3 8x 4 9x 5 8x 6 F 2 1 (x 3 ; x 2 ) ! F 2 1 (x 1 ; x 4 ) V F 2 1 (x 1 ; x 5 ) ! F 2 1 (x 6 ; x 2 ) 65 L a19 , L 0 , ‘a 0 . : d . (1) d = 0 , , , 0 = , ‘a 0 (2) d n , d = n + 1 . a19 : : 1 , 1 _ 2 , 1 ^ 2 , 1 ! 2 , 1 $ 2 , 9x 1 , 8x 1 . 66 ( 1) a22 a20 L 0 1 ; 0 2 , 1 ‘a 0 1 , 2 ‘a 0 2 . 0 1 ; 0 2 : Q 1 v 1 Q 2 v 2 Q m v m 00 1 Q m+1 v m+1 Q m+2 v m+2 Q m+n v m+n 00 2 : Q i 8 9, v i (1 i m + n). 00 1 00 2 . 67 ( 2) (2.1) : 1 , ‘a :Q 1 v 1 Q 2 v 2 Q m v m 00 1 . ‘a Q 1 v 1 Q 2 v 2 Q m v m : 00 1 . : Q i = 8 > < > : 8 Q i 9 9 Q i 8 Q 1 v 1 Q 2 v 2 Q m v m : 00 1 . 68 ( 3) (2.2) 1 _ 2 . ‘a(Q 1 v 1 Q m v m 00 1 )_ (Q m+1 v m+1 Q m+n v m+n 00 2 ) ‘a Q 1 v 0 1 Q m v 0 m 00 1 (v m =v 0 m ) (v 1 =v 0 1 ) _ Q m+1 v 0 m+1 Q m+n v 0 m+n 00 2 (v m+n =v 0 m+n ) (v m+1 =v 0 m+1 ) : v 0 1 ; v 0 2 ; ; v 0 m+n L , 0 1 0 2 . 69 ( 4) a22 12 : ‘aQ 1 v 0 1 Q m v 0 m Q m+1 v 0 m+1 Q m+n v 0 m+n 00 1 (v m =v 0 m ) (v 1 =v 0 1 ) _ 00 2 (v m+n =v 0 m+n ) (v m+1 =v 0 m+1 ) ! . 70 ( 4) (2.3) 1 ^ 2 , (2.2) . (2.4) 1 ! 2 , 6 10 . (2.5) 1 $ 2 , ‘a ( 1 ! 2 ) ^ ( 2 ! 1 ). a22 (2.3) (2.4) : ‘a . (2.6) 8x 1 9x 1 , a22 1 (6,7) . , . 71 11 n a19 0 a21 . (1) , n 1 , a19 Q n , Q n . (2) , n 1 , a19 P n , P n . : 8x 1 8x 2 (F 1 (x 1 )!F 1 (x 2 )) Q 1 . 9x 3 9x 1 8x 1 8x 2 (F 1 (x 1 )!F 1 (x 2 )) P 2 . 72 N L 12 N L a19 , ; ‘ N L , N L a19 a98 , ‘ N L . : 1 ; 2 ; ; n ‘ N L ‘ N L 1 ! 2 ! ! n ! ‘ N L ( 1 ^ 2 ^ ^ n )! 73 p.560(p.185) 17. (1), (2), (3) 18. (1), (3) 19. (2),(3) 74 75