ממן11

ממן11 - 11"...

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Unformatted text preview: 11 " 1 ." ," , , , , , : 2 : . X = {1}, Y = {1,2}, A = {2} X - A = {1} - {2} = {1} = {1,2} - {2} = Y - A X = {1} {1,2} = Y : . X = {1}, Y = {2}, A = {3} A - X = {3} - {1} = {3} = {3} - {2} = A - Y X = {1} {2} = Y , . A = , B = . A B . . A ( B - A) = ( - ) = = B , x A . x B , B x B - A , x B . x A , . x A ( B - A) .1 .2 .3 (i) . x A ( B - A) , , , : .- . y B - A y A - . y A ( B - A) . y B , A B , y A , . y B , , y B - A , . A ( B - A) = B ,- . . P (B ) P ( A) , , B A . {} P ( A) P ( B ) , P ( A) P ( B ) - (i) .4 (ii) ,(i) ) X P ( A) P ( B ) , . A B = - . X = .( : P ( A) P ( B ) - , . X B X A , X P (B ) X P ( A) , - , . X = , A B = . X A B . P ( A) P ( B ) {} , P ( A) P ( B ) (ii) . P ( A) P( B ) = {} ,- A B = ( A - B ) ( B - A) = = ( A B' ) ( B A' ) = = [ A ( B A' )] [ B '( B A' )] = = [( A B) ( A A' )] [( B 'B ) ( B ' A' )] = = [( A B) U ] [U ( B ' A' )] = = ( A B) ( B ' A' ) = = ( A B) ( A'B ' ) = = ( A B) ( A B )' = = ( A B) - ( A B) 3 . ( ) ( A - B = A B' ) 1 ) ( ("-") ( A A' = U ) ( A U = A) ( ) ( A' B ' = ( A B )' : ) ( A - B = A B' ) A B = [ A ( A B )] [ B ( A B )] = = ( A B) ( A B) = = [( A B ) ( A B )] U = = [( A B ) ( A B )] [( A B ) ( A B )' ] = = ( A B ) [( A B ) ( A B )' ] = = ( A B) ( A B) . ( A ( A B) = A ) ( ) ( A U = A) ( A A' = U ) 2 ( ) A B = ( A B) ( A B )' ) (' .3 4 : A0 = {0,1}, A4 = {4,5,8}, A1 = {1,2}, A2 = {2,3,4}, A3 = {3,4,6}, A7 = {7,8,14} : D0 = A1 - ( A0 A2 ) = {1,2} - ({0,1} {2,3,4}) = = {1,2} - {0,1,2,3,4} = D1 = A2 - ( A1 A3 ) = {2,3,4} - ({1,2} {3,4,6}) = = {2,3,4} - {1,2,3,4,6} = D2 = A3 - ( A2 A4 ) = {3,4,6} - ({2,3,4} {4,5,8}) = = {3,4,6} - {2,3,4,5,8} = {6} D3 = A4 - ( A3 A5 ) = {4,5,8} - ({3,4,6} {5,6,10}) = = {4,5,8} - {3,4,5,6,10} = {8} D4 = A5 - ( A4 A6 ) = {5,6,10} - ({4,5,8} {6,7,12}) = = {5,6,10} - {4,5,6,7,8,12} = {10} D5 = A6 - ( A5 A7 ) = {6,7,12} - ({5,6,10} {7,8,14}) = = {6,7,12} - {5,6,7,8,10,14} = {12} A5 = {5,6,10}, A6 = {6,7,12}, .1 nB YA n = A0 A1 A2 A3 = {0,1} {1,2} {2,3,4} {3,4,6} = {0,1,2,3,4,6} .2 ( ) ( A B) ( A B' ) = A ( B B' ) = ( B B' = ) = A = ( ) =A nB A n = A0 A1 A2 A3 = {0,1} {1,2} {2,3,4} {3,4,6} = . .3 ( Dn = An +1 - ( An An + 2 )4) ( An = {n, n + 1,2n} ) m {n + 1, n + 2,2n + 2} - ({n, n + 1,2n} {n + 2, n + 3,2n + 4}) ( :) : Dn = {2 x + 6 | x N } m {n + 1, n+ 2,2n + 2} - {n, n + 1, n + 2, n + 3,2n,2n + 4} n N () m 2n + 2} { : ( {2n + 2} - 2n + 2 ) m = 2n + 2 . n N m D , . m Dn ) m An +1 - ( An An + 2 n nN , ,' , m D1 m D0 . n 1 n 0 :( n n + 1 ) n + 1 2n n 2n , n = 1 n = 0 . n + 1 = 2n n = 2n : An - , . , . n, n + 1,2n : , Dn - m - x N , {n - 2 | n N , n 0, n 1} = N : , . x + 2 = n m = 2( x + 2) + 2 = 2 x + 6 . m {2 x + 6 | x N } , N - x : , : n N . m = 2 x + 6 x N , m {2 x + 6 | x N } , . m = 2(n - 2) + 6 = 2n + 2 : , n - 2 = x - m {2n + 2} m {n + 1, n + 2,2n + 2} - {n, n + 1, n + 2, n + 3,2n,2n + 4} m {n + 1, n + 2,2n + 2} - ({n, n + 1,2n} {n + 2, n + 3,2n + 4}) m An +1 - ( An An + 2 ) m Dn . m Dn , n N - nN . nN Dn = {2 x + 6 | x N } , ...
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