: a b c d 2: x x y y 3: x y w 3.. 3.2 2. 3.3 3. 3.4 (x, y,, w) = (,,, )xy w (,,, )xȳ w (,,, ) xy w (,,, )xy w (,,, )xȳ w (,,, ) xy w (,,, )xy w (,,, ) xȳw (,,, )xȳw (,,, ) xyw, F F = xy w x w xy w xy w xȳ w xy w xy w xȳw xȳw xyw, F F 2 = F = xȳ w xȳ w xy w xȳ w xȳ w xyw F 2 =(x y w)( x y w)(x ȳ w)(x y w)(x y w)( x ȳ w)
3.5 n (x,x 2,...,x n ) n, (x,x 2,...,x n )= (c 2,c 3,...,c n) (x,c 2,...,c n ) x c2 2 xc3 3 xcn n., 2 n., 2 n., n, 2 n. 3.6 () = x y x = x xy, = x xy xy =( x)y = y xy, = x y xy. (2) g = xy( w) w( x ȳ) =xy(w ) w(xy ) xy(w ) w(xy ) = g = xyw xy xyw w = xyw xyw xy w = xy w. 3.7 (xy) = () xȳ () xȳ () xy () xy ()xȳ ()xȳ ()xy ()xy = xȳ xy ( ) = xȳ xȳ xy xy xȳ xy = (x y )(x y )(x ȳ )(x ȳ )( x y )( x ȳ ) ( ) = x(y ) =xy x ( ) 2
3.8 () n ( ) ( ) ( ) = ( ) ( ) =. n ( ) ( ) = =. (2) x x x x (3) x x = x = x x x =. x = x. (4) (x y)(y )( x) = (xy x yy y)( x) = xy x yy y xxy xx xyy xy = xy xy x x xy xy y y = (5) (a) (x y = x ) (y = ). x x x y = x x y =, x y = x y =. (b) (y = ) (x y = x ). x x y = x. (a), (b) (x y = x ) (y = ). (6) (a) ( = g h) (g = h). = g h, h = g h h = g h h h = g,. (b) (g = h) ( = g h). g = h, h,. g = h g h = h h g h = (a), (b) ( = g h) (g = h). 3
(7) = (x a)(x b) =xx xa xb ab = x xa xb ab = (ā b)x ab =(a ) bx ab = x ax bx ab,. (8) = (x y) (y ) =(x y xy) (y y) = x xy y y y = x xy y = x xy y = xȳ ȳ = x(y ) (y ) = x xy y,. (9) xy y x = (xy y xy y) x = (xy y xy) x (xy y xy) = xy y xy x xy xy xy = xy y x,. 3.9 4., x =,y =, =,., x (y ) (x y) (x ).. 4: x y y x (y ) x y x (x y) (x ) 3. = x x 2 x 4 x 2 x 3 x 4 (x 2 x 3 x 4 x x 2 x 3 x 4 ), x 4 x 2 x 3 x 4 x x 2 x 3 x 4 (x 2 x 3 x x 2 x 3 ), F.. F = x x 2 x 4 x 2 x 3 x 4 x 4 (x 2 x 3 x x 2 x 3 ) 4
x 2 x 4 x 2 3 x 4 x 2 x 3 x 4 x 2 x 3 : 3. 3. (a) = xy x xw y yw w x =,, = y yw w = y w y yw w, y =,,,,. = w = w w = w w = = w w w = w = w = =,. =, = = w, = w = w = = w w =, 2 B. (b) g = x y w (a), g = y w g = y w =ḡ g = w g = w =ḡ g = w g = w =ḡ, 3 B. 5
g x x y y y y w w w w 2: 3: 3.2 x < <x n, ROB 2 n, x n+ < <x 2n, 2 n,., (2 n ) 2+2=2 n+. 3.3,g x =, = H(( x =),g( x = )) H(( x =),g( x = )) = H(( x =),g( x = )) =,g x =,,. = H(( x =),g( x = )) H(( x =),g( x = )) = H(( x =),g( x = )) = 3.4., x,x 2,x 3,x 4 = x x 2 x 3 x 4. a b = ā b a b, (x x 2 ) (x 3 x 4 ) = (x x 2 ) (x 3 x 4 ) (x x 2 ) (x 3 x 4 ). 4. 6
sw sw2 sw3 sw4 4: 3.4 sw, sw2, sw3, sw4, Lamp. 4. 3.5, (x,x 2,...,x n )= (c,c 2,...,c n)., = (c,c 2,...,c n) (c,c 2,...,c n )x c xc2 2 xcn n (c,c 2,...,c n )x c xc2 2 xcn n = (,,...,) x x 2... x n (,,...,)x x 2 x n (,,,...,) x x 2 x 3 x n (,,...,, ) x x 2 x n x n (,,,...,)x x 2 x 3 x n (,,,,...,)x x 2 x 3 x 4 x n (,,...,,, ) x x 2 x n 2 x n x n (,,...,)x x 2 x n = a ( x )( x 2 ) ( x n ) a x ( x 2 ) ( x n ) a 2 ( x )x 2 ( x 3 ) ( x n ) a n ( x )( x 2 ) ( x n )x n a 2 x x 2 ( x 3 ) ( x n ) a 3 x ( x 2 )x 3 ( x 4 ) ( x n ) a n,n ( x )( x 2 ) ( x n 2 )x n x n a 2 n x x 2 x n = a (a x a 2 x 2 a n x n ) (a 2 x x 2 a 3 x x 3 a n,n x n x n ) a 2 n x x 2 x n 3.6 = xy = xy g = xy u = xy ū 7
5: x y xy = x y u xy ū = g 5. 3.7 NAN,,.,., NAN, 5. 5: NAN w =, 6. (x, y,, ) = (x xy) (x ȳ) = x xy x ȳ = x( ) xy ȳ = x xy ȳ, w =, 7. (x, y,, ) = =, 8. x 2 4 5 7 6 7 y 3 6 6: (x, y,, ) 7: (x, y,, ) 8
x w y 8: 6: A B C A B C 3.8 9., 2 NAN.,,. A =, B., A =, B. A B.,., NAN OR., NOT., B = B =. B =, x NAN =. B =, y NAN =., =.,. 6. 3.9 NAN,,,., A=,, 2, 6,. NAN,., NAN.,. 9
C A B B 9: 3.8 : 3.8 C 4 4 (,B,C,) B 8 8 9 C 3 3 5 5 : 3 = C 4 = C 3 = C( C ) =C 5 = 3 = ( C ) = C 8 = B( C ) = B C B (,B,C,) = 4 5 8 = C C B C B A=, 6, 8., NAN 2. B 2 2 C 4 4 B C 9 (,B,C,) C 3 3 5 5 2:. 2 = BC
A C B 3: 2 = B BC 3 = C BC 4 = C 2 3 5 = 2 3 (,B,C,) = C 2 3 2 3 = BC BC B C 3. 3.2 I H Ī K I H K,, = I H (Ī K) I H K = I H Ī K I H K = I H Ī H Ī K I H K I H K = H Ī K I H = H K Ī IH = H K Ī H = Ī K =. 3.2 xȳ xy =, x x = y 2. 2,
( 2 ) = x x = x(xȳ xy) x(xȳ xy) = x( x y)(x ȳ) xy = xy(x ȳ) xy = (x x)y = y, xȳ xy =, x x = y. 3.22 x y =, x y = 2. 2 ( 2 ) = x y = x y(x y) = x xy y = x y, 2 =, x y =,, =., (x, y, ) =(,, ), (,, ), (,, ). 3.23 x xy =, xy = x 2. x =. x = 2, y =, y =., (x, y, ) =(,, ). 2