. , , , , , , , , ? (. 1).
1
= { , , }, = { , , , } , , , , . ( ) B.
. ´ , (, ), , Î , Î , .. ´ B = {(, ) | Î , Î }.
, , ´ Æ = Æ ´ = Æ.
, , .
. = {1, 2, 3}, = {2, 3, 4, 5}, ´ B = {(1, 2), (1, 3), (1, 4), (1, 5), (2, 2), (2, 3), (2, 4), (2, 5), (3, 2), (3, 3), (3, 4), (3, 5)}.
, , , (2, 3) ≠ (3, 2).
A B , ´ , , . . 1 ´ = [0, 2], B = [1, 2]. . 2 ´ = {0, 1, 2}, B = [1, 2].
2 2
1 1
0 1 2 0 1 2
. 9 . 10
.
, .. , A ´ ≠ ´ . , , : , :
( ) ´ = (A ´ ) ( ´ ), ´ ( ) = ( ´ ) ( ´ );
( ) ´ = (A ´ ) ( ´ ), ´ ( ) = ( ´ ) ( ´ );
( \ ) ´ = (A ´ ) \ ( ´ ), ´ ( \ ) = ( ´ ) \ ( ´ ).
.
= {1, 2}, B = {2, 3} C = { a } ( ) ´ = (A ´ ) ( ´ ).
{1, 2, 3} = {(1, a); (2, a); (3, a)}.
|
|
, {(1, a); (2, a)}, {(2, a); (3, a)}
{(1, a); (2, a); (3, a)}.
, . , .
, , , . :
( ) ( )
( ) .
, . , .
(, , , n ).
. A 1 ´ A 2 ´ ´ An A 1, A 2, , An (a 1, a 2, , an), 1 Î 1, 2 Î 2, , n Î n. n, ..
A 1 ´ A 2 ´ ´ An = {( 1, 2, , n)| 1 Î 1, 2 Î 2, , n Î n }.
. = {1, 2, 3}, = {3, 5, 7}, C = {4, 6}. A ´ ´ .
A ´ = {(1, 3), (1, 5), (1, 7), (2, 3), (2, 5), (2, 7), (3, 3), (3, 5), (3, 7)}.
A ´ ´ = {(1, 3, 4), (1, 5, 4), (1, 7, 4), (2, 3, 4), (2, 5, 4), (2, 7, 4), (3, 3, 4), (3, 5, 4), (3, 7, 4), (1, 3, 6), (1, 5, 6), (1, 7, 6), (2, 3, 6), (2, 5, 6), (2, 7, 6), (3, 3, 6), (3, 5, 6), (3, 7, 6)}.