ÿþK u r s w y r ó w n a w c z y z m a t e m a t y k i
m a t e r i a By p o m o c n i c z e
U r s z u l a C i e l n i a k
I . R a c h u n e k z b i o r ó w
S G H W a r s z a w a 2 0 1 0
A , B , C , . . . ,
a , b , c , . . .
x A x " A
x A x " A
/
"
A = { 1 , 3 , 5 } ,
B = { x " R : x 3 }
A B
A B
A = B Ô! "x " A ( x " A Ô! x " B ) .
A B A
B
A ‚" B .
A B
A B
A *" B = { x : x " A (" x " B } .
A *" B = B *" A
A *" ( B *" C ) = ( A *" B ) *" C
" *" A = A
A *" A = A
A = { - 2 , - 1 , 0 , 1 , 2 } B = - 2 , 2 ) A
B
A *" B = - 2 , 2 ) .
A B
A B
A )" B = { x : x " A '" x " B } .
A )" B = B )" A
A )" ( B *" C ) = ( A )" B ) )" C
" )" A = "
A )" A = A
A B
A )" B = { - 2 , - 1 , 0 , 1 } .
A B
A B
A - B = { x : x " A '" x " B } .
/
A - B = B - A A = B
A - " = A " - A = "
A B
A - B = { 2 } ,
B A
B - A = ( - 2 , - 1 ) *" ( - 1 , 0 ) *" ( 0 , 1 ) *" ( 1 , 2 ) .
A B
A )" B = ".
A , B , . . . X
X
A X
A A
A = X - A .
A - B = A )" B
A *" A = X
A )" A = "
X = " " = X
( A ) = A
( A *" B ) = A )" B
( A )" B ) = A *" B
A B
A = R - { - 2 , - 1 , 0 , 1 , 2 } ,
B = ( - ", - 2 ) *" 2 , + ") .
A B
A × B = { ( x , y ) : x " A '" y " B } .
A n B m A × B
n · m
A × B A B
- 2 , - 1 , 0 , 1
2 - 2 , 2 )
A *" B A )" B A - B B - A A
A = ( 2 , 4 B = - 1 ; 3 , 5
A = 0 , 3 ) *" ( 4 , 5 ) B = ( 1 ; 4 , 5
A = ( - ", 4 B = ( 0 , 6
B *" ( A )" B ) A )" ( B *" C ) ( B - A ) )" C B *" ( C - A )
A = { 0 , 1 , 2 , 3 , 4 } B = { - 2 , 0 , 2 } C = { 3 , 4 , 5 }
A = ( - ", 5 ) B = ( 2 , + ") C = 3 , 4 )
A = ( - 2 , 6 B = 1 , 6 C = 6 , + ")
A × B
A = ( 1 , 5 B = - 1 , 1
A = ( - 3 , - 2 ) )" 0 , 2 B = - 3 , 3 )
A = { x " R : x 0 } B = { - 2 , 0 , 2 }
A = { ( x , y ) " R 2 : 3 x - y - 3 } B = { ( x , y ) " R 2 : y 0 }
A , B , C
B - A = B / ( B )" A )
B = ( B - A ) *" ( A )" B )
A )" B = A - B
( A - B ) - C ) = A - ( B *" C )
( A *" C ) - B = [ A - ( A )" B ) ] *" [ C - ( C )" B ) ]
( A *" B ) = A )" B
( A )" B ) = A *" B
A *" B = - 1 , 4 ; A )" B = ( 2 ; 3 , 5 ; A - B = ( 3 , 5 ; 4 ; B - A = - 1 , 2 ; A =
( - ", 2 *" ( 4 , + ")
A *" B = ( 0 , 5 ) ; A )" B = ( 1 , 3 ) *" ( 4 ; 4 , 5 ; A - B = 0 , 1 *" ( 4 , 5 ; 5 ) ; B - A =
3 , 4 ; A = ( - ", 0 ) *" 3 , 4 *" 5 , + ")
A *" B = ( - ", 6 ; A )" B = ( 0 , 4 ) ; A - B = ( - ", 0 ; B - A = ( 4 , 6 ; A =
( 4 , + ")
B *"( A )"B ) = B ; A )"( B *"C ) = A )"{ 0 , - 2 , 2 , 3 , 4 , 5 } = { 0 , 2 , 3 , 4 } ; ( B - A ) )"C =
{ - 2 } )" C = "; B *" ( C - A ) = B *" { 5 } = { - 2 , 0 , 2 , 5 }
B *"( A )"B ) = B ; A )"( B *"C ) = A )"B = ( 2 , 5 ) ; ( B - A ) )"C = 5 , + ") )" 3 , 4 ) =
"; B *" ( C - A ) = ( 2 , + ") *" " = ( 2 , + ")
B *" ( A )" B ) = B ; A )" ( B *" C ) = A )" 5 , + ") = 1 , 6 ; ( B - A ) )" C = " )" C =
"; B *" ( C - A ) = B *" ( 6 , + ") = 1 , + ")
( A )" B )
A *" B
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