Компьютерная математика: Часть 1. Теория множеств и комбинаторика. Волченская Т.В - 86 стр.

UptoLike

ВУЗ: 

ПГУ | Пенза

Составители: 

Рубрика: 

86
3.
S
2
= {(x, x); (x, y);
(x, z); (y, x); (y, y); (y, z)
(z, x); (z, y); (z, z) }.
Ответы
Упражнения 2.1
1. Р = {(2, 2), (2, 4),
(2, 6), (2, 8), (4, 4), (4, 6),
(4, 8), (6, 6), (6, 8), (8, 8)}.
2.
ρ = {(2, 4), (2, 6),
(2, 8), (4, 6), (4, 8), (6, 8)}.
ρ
–1
= {(4, 2), (6, 2),
(8, 2), (6, 4), (8, 4), (8, 6)}.
3. Р
= {((x, y), z)) : x < y,
x
≤ z < y}, P = { ((1, 2 ), 1),
((1, 3), 1), ((1, 3), 2), ((1, 4), 1), ((1, 4), 2), ((1, 4), 3),
((1, 5), 1), ((1, 5), 2), ((1, 5), 3), ((1, 5), 4), ((2, 3), 2),
((2, 4), 2), ((2, 4), 3), ((2, 5), 2), ((2, 5), 3), ((2, 5), 4),
((3, 4), 3), ((3, 5), 3), ((3, 5), 4), ((4, 5), 4)}.
4. K
⊆ S×S и K = {((x
s
, y
s
), (x
t
, y
t
)) : x
s
= x
t
± 1,
y
s
= y
t
± 2 или x
s
= x
t
± 2,
y
s
= y
t
± 1.
5. I = {(a, a), (b, b),
(c, c)}, U = {(a, a), (a, b),
(a, c), (b, a), (b, b), (b, c),
(c, a), (c, b), (c, c)}.
6. a) M = {1, 2, 3, 4, 6};
б) R = {(1, 1), (1, 3), (2, 2),
(2, 4), (2, 6), (3, 1), (3, 3),
(4, 2), (4, 4), (4, 6), (6, 2),
(6, 4), (6, 6)};
в) D(M) = {1, 2, 3, 4, 6},
ℜ (M) = {1, 2, 3, 4, 6}. 
        3. S2              =             {(x,             x);            (x,         y);
(x,          z);          (y,          x);          (y,            y);         (y,    z)
(z, x); (z, y); (z, z) }.

                                         Ответы

                                     Упражнения 2.1
       1. Р = {(2, 2), (2, 4),
(2, 6), (2, 8), (4, 4), (4, 6),
(4, 8), (6, 6), (6, 8), (8, 8)}.
       2. ρ = {(2, 4), (2, 6),
(2, 8), (4, 6), (4, 8), (6, 8)}.
        ρ–1 = {(4, 2), (6, 2),
(8, 2), (6, 4), (8, 4), (8, 6)}.

       3. Р = {((x, y), z)) : x < y,
x ≤ z < y}, P = { ((1, 2 ), 1),
((1, 3), 1), ((1, 3), 2), ((1, 4), 1), ((1, 4), 2), ((1, 4), 3),
((1, 5), 1), ((1, 5), 2), ((1, 5), 3), ((1, 5), 4), ((2, 3), 2),
((2, 4), 2), ((2, 4), 3), ((2, 5), 2), ((2, 5), 3), ((2, 5), 4),
((3, 4), 3), ((3, 5), 3), ((3, 5), 4), ((4, 5), 4)}.
        4. K ⊆ S×S и K = {((xs, ys), (xt, yt)) : xs = xt ± 1,
ys = yt ± 2 или xs = xt ± 2,
ys = yt ± 1.

        5. I = {(a, a), (b, b),
(c, c)}, U = {(a, a), (a, b),
(a, c), (b, a), (b, b), (b, c),
(c, a), (c, b), (c, c)}.
        6. a) M = {1, 2, 3, 4, 6};
б) R = {(1, 1), (1, 3), (2, 2),
(2, 4), (2, 6), (3, 1), (3, 3),
(4, 2), (4, 4), (4, 6), (6, 2),
(6, 4), (6, 6)};

     в) D(M) = {1, 2, 3, 4, 6},
ℜ (M) = {1, 2, 3, 4, 6}.

                                           86

Страницы