³ ᒺ. ³ , . ¢ . , . : , , . ³ .
õ
1. A Ì X ´ Y. X {x2, x3}.
AÌX´Y; xiÎX, xi , (xi), yÎY , (xi, y) Î.
- Y Y/A. .
:
X={ x1, x2, x3, x4, x5};
Y= { y1, y2, y3, y4};
A= {(x1, y1), (x1, y3), (x2, y1), (x2, y3), (x2, y4), (x3, y1), (x3, y2), (x3, y4),
(x4, y3), (x5, y2), (x5, y4)}.
X , - Y/A:
x1 x2 x3 x4 x5
{y1,y3} { y1,y3, y4} { y1,y2, y4} {y3} { y2, y4}.
ᒺ B Ì X A(B) , A(B)= . ,
A(x2, x3) = A(x2) È A(x3) = { y1, y2, y3, y4}.
õ
1. ,
= {1, 2, 3}:
) {(1, 1), (1, 2), (1, 3)};
) {(1, 1), (2, 1), (2, 2), (2, 3)};
) {(1, 1), (1, 2), (1, 3), (2, 2), (2, 3), (3, 3)};
) {(1, 3), (3, 1)}.
2. R, : (a, b, c)ÎR,
0 < a < b < c < 5.
3. X= {x1, x2, x3, x4, x5, x6}, Y = {y1, y2, y3, y4}. A = {(x1,y2), (x2, y1 ), (x2, y2), (x4, y2), (x4, y3), (x5, y1), (x5, y3)}. :
) ;
) X;
) X¢ = {x1, x4}; X¢¢ = {x2, x3, x5};
) ;
) A-1.
4. , (. 7), . ?
. 7.
5. R. x y, (x, y) Î A. ³ , (, ).
|
|
A = {(x, y) Î R´R| P(x, y)},
, .
6. ( , , ):
) {(x, y) Î R´R| x = y};
) {(x, y) Î R´R| y ³ x};
) {(x, y) Î R´R| x ³ 0; y £ x x + y £ 1}.
7. , . 8.
. 8.
8. , . ³ A = {1, 2, 3, 4}:
) {(2, 2), (2, 3), (2, 4), (3, 2), (3, 3), (3,4)};
) {(1, 1), (1, 2), (2, 1), (2, 2), (3, 3), (4, 4)};
) {(2,4), (4,2)};
) {(1, 2), (2, 3), (3, 4)};
) {(1, 1), (2, 2), (3, 3), (4, 4)};
e) {(1, 3), (1, 4), (2, 3), (2, 4), (3, 1), (3, 4)}.
9. . ¢¢Գ- 1¢¢.
Գ- 1
̳ | ||
¢¢¢¢ | ||
¢¢¢¢ | ||
¢¢Sit¢¢ | ||
¢¢Sit¢¢ | ||
¢¢House¢¢ | ||
¢¢House¢¢ |
, , . .
Գ- 2
̳ | ||
¢¢¢¢ | ||
¢¢Virta¢¢ | ||
¢¢Virta¢¢ | ||
¢¢¢¢ | ||
¢¢¢¢ | ||
¢¢¢¢ | ||
¢¢¢¢ |
ᒺ, ¢¢Գ- 1¢¢ ¢¢Գ- 2¢¢. , ¢ ¢¢Գ- 3¢¢.
õ
1. :
) (AB)-1 = B-1A-1;
) (A È B)-1 = A-1 È B-1;
) (A Ç B)-1 = A-1 Ç B-1;
) (A-1)-1 = A.
2. :
) A B ,
A È B, A Ç B, AB;
) A B , A È B, A Ç B;
) A B ,
A È B, A Ç B;
) A B ,
A Ç B.
3. ( , , ):
) {(x, y) Î R´R| y ³ x x ³ 0};
) {(x, y) Î R´R| x2 + y2 =1}.
5. 璺 ¢¢Գ- 3¢¢ ¢¢Գ-¢¢. ³ ¢¢Գ-¢¢ :
|
|
Գ-
¢¢¢¢ | 784-556 |
¢¢¢¢ | 145-134 |
¢¢Sit¢¢ | 356-777 |
¢¢House¢¢ | 122-890 |
¢¢¢¢ | 555-78-12 |
¢¢Virta¢¢ | 233-77-77 |
¢¢¢¢ | 550-09-09 |
, 璺, ¢¢Գ--¢¢.
5. ¢¢Գ--¢¢ :
) = ;
) = , = ;
) = .
8
ϳ , . , , , , .
. 9.
-. -:
. 10. -
õ
1. ³
3, 1, 0, 1, 8, 6, 5, -5.
:
1) ;
2) ;
3) , ;
4) i ;
2-4 , n.
n´n (n ).
. 11.
k . :
k = A[i],
A[i] = A[i+1],
A[i+1] = k,
. 12.
A[ 1 ] A[ n ] n, . - :
. 13. -
õ
1. - .
2. - .
3. - , , , , , , .
4. - m*n max min . , max min .
5. - , , , 䒺 , , , .
6. m*n . . -.
õ
1. a, b, c. . -.
2. - ax + b = 0.
3. - .
4. , . ϳ , , . -.
|
|
5. m*n . . -.
6. , 1. ϳ : 5 1, 5 0. , , , 0 1. -.
9