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Дискретна математика 2 семестр

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Задати орієнтований граф за допомогою матриці суміжності.

	a	b	c	d	f	g	h	j
a	0	1	1	1	0	0	0	0
b	0	0	0	1	0	2	1	0
c	0	0	0	0	0	1	0	0
d	1	0	0	1	0		1	1
f	0	1	0	0	0	1	1	0
g	1	0	0	0	2	0	0	0
h	0	0	0	0	1	0	0	1
j	0	0	0	0	0	0	2	1

	a	b	c	d	f	g	h	j
a	0	1	1	1	0	0	0	0
b	0	0	0	1	0	1	2	0
c	0	0	0	0	0	1	0	0
d	1	0	0	1	0	0	1	1
f	0	0	0	0	1	1	1	0
g	1	0	0	0	2	0	0	0
h	0	0	0	0	1	0	0	0
j	0	0	0	0	0	0	1	2

	a	b	c	d	f	g	h	j
a	0	1	1	1	0	0	0	0
b	0	0	0	1	0	1	2	0
c	0	0	0	0	0	1	0	0
d	1	0	0	1	0	0	1	1
f	0	1	0	0	1	1	1	0
g	1	0	0	0	2	0	0	0
h	0	0	0	0	1	0	0	1
j	0	0	0	0	0	0	2	1

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Задати орієнтований граф за допомогою матриці інцидентності.

	e_1	e_2	e_3	e_4	e_5	e_6	e_7	e_8	e_9	$e_{10}$ e_{10}	$e_{11}$ e_{11}	$e_{12}$ e_{12}	$e_{13}$ e_{13}	$e_{14}$ e_{14}	$e_{15}$ e_{15}	$e_{16}$ e_{16}
a	-1	1	1	0	0	0	0	0	1	0	0	0	0	0	0	0
b	0	0	-1	0	1	1	1	-1	0	0	0	0	0	1	0	0
c	0	-1	0	1	0	0	0	0	0	0	0	0	0	0	0	0
d	1	0	0	0	-1	0	0	0	-1	0	1	1	0	0	0	0
f	0	0	0	0	0	0	-1	1	0	1	0	0	0	0	0	2
g	0	0	0	-1	0	-1	1	0	0	0	0	0	0	0	0	0
h	0	0	0	0	0	0	0	0	0	-1	-1	0	1	-1	0	0
j	0	0	0	0	0	0	0	0	0	0	0	-1	-1	0	2	0

	e_1	e_2	e_3	e_4	e_5	e_6	e_7	e_8	e_9	$e_{10}$ e_{10}	$e_{11}$ e_{11}	$e_{12}$ e_{12}	$e_{13}$ e_{13}	$e_{14}$ e_{14}	$e_{15}$ e_{15}	$e_{16}$ e_{16}
a	-1	1	1	0	0	0	0	0	1	0	0	0	0	0	0	0
b	0	0	-1	0	1	1	0	-1	0	0	0	0	0	1	0	0
c	0	-1	0	1	0	0	0	0	0	0	0	0	0	0	0	0
d	1	0	0	0	-1	0	0	0	-1	0	1	1	0	0	0	0
f	0	0	0	0	0	0	-1	1	0	1	0	0	0	0	0	2
g	0	0	0	-1	0	-1	1	0	0	0	0	0	0	0	0	0
h	0	0	0	0	0	0	0	0	0	-1	-1	0	1	-1	0	0
j	0	0	0	0	0	0	0	0	0	0	0	-1	-1	0	2	0

	e_1	e_2	e_3	e_4	e_5	e_6	e_7	e_8	e_9	$e_{10}$ e_{10}	$e_{11}$ e_{11}	$e_{12}$ e_{12}	$e_{13}$ e_{13}	$e_{14}$ e_{14}	$e_{15}$ e_{15}	$e_{16}$ e_{16}
a	-1	1	1	0	0	0	0	0	1	0	0	0	0	0	0	0
b	0	0	-1	0	1	1	0	-1	0	0	0	0	0	1	0	0
c	0	-1	0	1	0	0	0	0	0	0	0	0	0	0	0	0
d	1	0	0	0	-1	0	0	0	-1	0	-1	1	0	0	0	0
f	0	0	0	0	0	0	-1	1	0	1	0	0	0	0	0	2
g	0	0	0	-1	0	-1	1	0	0	0	0	0	0	0	0	0
h	0	0	0	0	0	0	0	0	0	-1	1	0	1	-1	0	0
j	0	0	0	0	0	0	0	0	0	0	0	-1	-1	0	2	0

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Задати неорієнтований граф за допомогою матриці інцидентності.

	e_1	e_2	e_3	e_4	e_5	e_6	e_7	e_8	e_9	$e_{10}$ e_{10}	$e_{11}$ e_{11}	$e_{1 2}$ e_{1 2}	$e_{1 3}$ e_{1 3}	$e_{14}$ e_{14}	$e_{1 5}$ e_{1 5}	$e_{1 6}$ e_{1 6}
a	1	1	1	0	0	0	0	0	1	0	0	0	0	0	0	0
b	0	0	1	0	1	1	0	1	0	0	0	0	0	1	0	0
c	0	1	0	1	0	0	0	0	0	0	0	0	0	0	0	0
d	1	0	0	0	1	0	0	0	1	0	1	1	0	0	0	0
f	0	0	0	0	0	0	1	1	0	1	0	0	0	0	0	2
g	0	0	0	1	0	1	1	0	0	0	0	0	0	0	0	0
h	0	0	0	0	0	0	0	0	0	1	1	0	1	1	0	0
j	0	0	0	0	0	0	0	0	0	0	0	1	1	0	2	0

	e_1	e_2	e_3	e_4	e_5	e_6	e_7	e_8	e_9	$e_{10}$ e_{10}	$e_{11}$ e_{11}	$e_{1 2}$ e_{1 2}	$e_{1 3}$ e_{1 3}	$e_{14}$ e_{14}	$e_{1 5}$ e_{1 5}	$e_{1 6}$ e_{1 6}
a	1	1	1	0	0	0	0	0	1	0	0	0	0	0	0	0
b	0	0	0	0	1	1	0	1	0	0	0	0	0	1	0	0
c	0	1	0	1	0	0	0	0	0	0	0	0	0	0	0	0
d	1	0	0	0	1	0	0	0	1	0	1	1	0	0	0	0
f	0	0	1	0	0	0	1	1	0	1	0	0	0	0	0	2
g	0	0	0	1	0	1	1	0	0	0	0	0	0	0	0	0
h	0	0	0	0	0	0	0	0	0	1	1	0	1	1	0	0
j	0	0	0	0	0	0	0	0	0	0	0	1	1	0	2	0

100%

	e_1	e_2	e_3	e_4	e_5	e_6	e_7	e_8	e_9	$e_{10}$ e_{10}	$e_{11}$ e_{11}	$e_{1 2}$ e_{1 2}	$e_{1 3}$ e_{1 3}	$e_{14}$ e_{14}	$e_{1 5}$ e_{1 5}	$e_{1 6}$ e_{1 6}
a	1	1	1	0	0	0	0	1	1	0	0	0	0	0	0	0
b	0	0	1	0	1	1	0	1	0	0	0	0	0	1	0	0
c	0	1	0	1	0	0	0	0	0	0	0	0	0	0	0	0
d	1	0	0	0	1	0	0	0	1	0	1	1	0	0	0	0
f	0	0	0	0	0	0	1	1	0	1	0	0	0	0	0	2
g	0	0	0	1	0	1	1	0	0	0	0	0	0	0	0	0
h	0	0	0	0	0	0	0	0	0	1	1	0	1	1	0	0
j	0	0	0	0	0	0	0	0	0	0	0	1	1	0	2	0

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Нехай задано орієнтований граф.

Визначити:

$deg^{+}(d)$ deg^{+}(d)

$deg^{-}(f)$ deg^{-}(f)

$deg^{-}(d)$ deg^{-}(d)

$deg^{+}(c)$ deg^{+}(c)

кількість вершин

$deg^{-}(c)$ deg^{-}(c)

$deg^{-}(b)$ deg^{-}(b)

кількість дуг

$deg^{+}(f)$ deg^{+}(f)

$deg^{-}(e)$ deg^{-}(e)

$deg^{+}(b)$ deg^{+}(b)

$deg^{-}(a)$ deg^{-}(a)

$deg^{+}(e)$ deg^{+}(e)

$deg^{+}(a)$ deg^{+}(a)

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Нехай задано неорієнтований граф.

Визначити:

кількість вершин графа

степінь вершини b

степінь вершини e

кількість ребер графа

степінь вершини f

степінь вершини c

степінь вершини a

степінь вершини d

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Поліномом Жегалкіна називають формулу

$P(\tilde{x}^n)=k_1 \oplus k_2 \oplus ... \oplus k_s$ P(\tilde{x}^n)=k_1 \oplus k_2 \oplus ... \oplus k_s , де k_1, k_2,..., k_s --попарно різні монотонні кон'юнкції змінних із множини $X=\{x_1,x_2,..., x_n\}$ X=\{x_1,x_2,..., x_n\} .

$P(\tilde{x}^n)=k_1 \vee k_2 \vee ... \vee k_s$ P(\tilde{x}^n)=k_1 \vee k_2 \vee ... \vee k_s , де k_1, k_2,..., k_s --попарно різні монотонні кон'юнкції змінних із множини $X=\{x_1,x_2,..., x_n\}$ X=\{x_1,x_2,..., x_n\} .

$P(\tilde{x}^n)=k_1 \oplus k_2 \oplus ... \oplus k_s$ P(\tilde{x}^n)=k_1 \oplus k_2 \oplus ... \oplus k_s , де k_1, k_2,..., k_s --попарно однакові монотонні кон'юнкції змінних із множини $X=\{x_1,x_2,..., x_n\}$ X=\{x_1,x_2,..., x_n\} .

$P(\tilde{x}^n)=k_1 k_2 ... k_s$ P(\tilde{x}^n)=k_1 k_2 ... k_s , де k_1, k_2,..., k_s --попарно різні монотонні кон'юнкції змінних із множини $X=\{x_1,x_2,..., x_n\}$ X=\{x_1,x_2,..., x_n\} .

$P(\tilde{x}^n)=k_1 \oplus k_2 \oplus ... \oplus k_s$ P(\tilde{x}^n)=k_1 \oplus k_2 \oplus ... \oplus k_s , де k_1, k_2,..., k_s --попарно різні монотонні диз'юнкції змінних із множини $X=\{x_1,x_2,..., x_n\}$ X=\{x_1,x_2,..., x_n\} .

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Методом невизначених коефіцієнтів знайти поліном Жегалкіна функції $f(\tilde{x}^3)=(00110100)$ f(\tilde{x}^3)=(00110100) .

$x_2\oplus x_2 x_3\oplus x_1 x_3 \oplus x_1 x_2 x_3$ x_2\oplus x_2 x_3\oplus x_1 x_3 \oplus x_1 x_2 x_3

$x_2\oplus x_3\oplus x_1 x_3 \oplus x_1 x_2 x_3$ x_2\oplus x_3\oplus x_1 x_3 \oplus x_1 x_2 x_3

$x_2\oplus x_1 x_2\oplus x_1 x_3 \oplus x_2 x_3$ x_2\oplus x_1 x_2\oplus x_1 x_3 \oplus x_2 x_3

$x_2\oplus x_1 x_2\oplus x_1 x_3 \oplus x_1 x_2 x_3$ x_2\oplus x_1 x_2\oplus x_1 x_3 \oplus x_1 x_2 x_3

$x_1\oplus x_1 x_2\oplus x_1 x_3 \oplus x_1 x_2 x_3$ x_1\oplus x_1 x_2\oplus x_1 x_3 \oplus x_1 x_2 x_3

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Досконалою кон'юнктивною нормальною формою називають

кон'юнктивну нормальну форму, у якої кожна елементарна кон'юнкція $d_j (j=\overline{1,s})$ d_j (j=\overline{1,s}) -- конституента нуля.

кон'юнктивну нормальну форму, у якої кожна елементарна диз'юнкція $d_j (j=\overline{1,s})$ d_j (j=\overline{1,s}) -- конституента нуля.

кон'юнктивну нормальну форму, у якої кожна елементарна диз'юнкція $d_j (j=\overline{1,s})$ d_j (j=\overline{1,s}) -- конституента одиниці.

кон'юнктивну нормальну форму, у якої кожна елементарна кон'юнкція $d_j (j=\overline{1,s})$ d_j (j=\overline{1,s}) -- конституента одиниці.

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Зобразити у вигляді досконалої кон'юнктивної нормальної форми функцію $f(\tilde{x}^3)=(00111001)$ f(\tilde{x}^3)=(00111001) .

$(x_1\vee \overline{x}_2\vee x_3)(x_1\vee x_2\vee \overline {x}_3)(\overline{x}_1\vee x_2\vee \overline{x}_3)(\overline{x}_1\vee \overline{x}_2\vee x_3)$ (x_1\vee \overline{x}_2\vee x_3)(x_1\vee x_2\vee \overline {x}_3)(\overline{x}_1\vee x_2\vee \overline{x}_3)(\overline{x}_1\vee \overline{x}_2\vee x_3)

$(x_1\vee x_2\vee x_3)(x_1\vee\overline{x}_2\vee \overline {x}_3)(\overline{x}_1\vee x_2\vee \overline{x}_3)(\overline{x}_1\vee \overline{x}_2\vee x_3)$ (x_1\vee x_2\vee x_3)(x_1\vee\overline{x}_2\vee \overline {x}_3)(\overline{x}_1\vee x_2\vee \overline{x}_3)(\overline{x}_1\vee \overline{x}_2\vee x_3)

$(x_1\vee x_2\vee x_3)(x_1\vee x_2\vee \overline {x}_3)(\overline{x}_1\vee x_2\vee \overline{x}_3)(\overline{x}_1\vee \overline{x}_2\vee x_3)$ (x_1\vee x_2\vee x_3)(x_1\vee x_2\vee \overline {x}_3)(\overline{x}_1\vee x_2\vee \overline{x}_3)(\overline{x}_1\vee \overline{x}_2\vee x_3)

$(x_1\vee x_2\vee x_3)(x_1\vee x_2\vee \overline {x}_3)(\overline{x}_1\vee x_2\vee \overline{x}_3)(\overline{x}_1\vee \overline{x}_2\vee \overline{x}_3)$ (x_1\vee x_2\vee x_3)(x_1\vee x_2\vee \overline {x}_3)(\overline{x}_1\vee x_2\vee \overline{x}_3)(\overline{x}_1\vee \overline{x}_2\vee \overline{x}_3)

$(x_1\vee x_2\vee x_3)(x_1\vee x_2\vee \overline {x}_3)(\overline{x}_1\vee \overline{x}_2\vee \overline{x}_3)(\overline{x}_1\vee \overline{x}_2\vee x_3)$ (x_1\vee x_2\vee x_3)(x_1\vee x_2\vee \overline {x}_3)(\overline{x}_1\vee \overline{x}_2\vee \overline{x}_3)(\overline{x}_1\vee \overline{x}_2\vee x_3)

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Виберіть чотири правилльні відповіді. Елементарними диз'юнкціями є

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	a	b	c	d	f	g	h	j
a	0	1	1	1	0	0	0	0
b	0	0	0	1	0	2	1	0
c	0	0	0	0	0	1	0	0
d	1	0	0	1	0		1	1
f	0	1	0	0	0	1	1	0
g	1	0	0	0	2	0	0	0
h	0	0	0	0	1	0	0	1
j	0	0	0	0	0	0	2	1

	a	b	c	d	f	g	h	j
a	0	1	1	1	0	0	0	0
b	0	0	0	1	0	1	2	0
c	0	0	0	0	0	1	0	0
d	1	0	0	1	0	0	1	1
f	0	0	0	0	1	1	1	0
g	1	0	0	0	2	0	0	0
h	0	0	0	0	1	0	0	0
j	0	0	0	0	0	0	1	2

	a	b	c	d	f	g	h	j
a	0	1	1	1	0	0	0	0
b	0	0	0	1	0	1	2	0
c	0	0	0	0	0	1	0	0
d	1	0	0	1	0	0	1	1
f	0	1	0	0	1	1	1	0
g	1	0	0	0	2	0	0	0
h	0	0	0	0	1	0	0	1
j	0	0	0	0	0	0	2	1

	e_1	e_2	e_3	e_4	e_5	e_6	e_7	e_8	e_9	$e_{10}$ e_{10}	$e_{11}$ e_{11}	$e_{12}$ e_{12}	$e_{13}$ e_{13}	$e_{14}$ e_{14}	$e_{15}$ e_{15}	$e_{16}$ e_{16}
a	-1	1	1	0	0	0	0	0	1	0	0	0	0	0	0	0
b	0	0	-1	0	1	1	1	-1	0	0	0	0	0	1	0	0
c	0	-1	0	1	0	0	0	0	0	0	0	0	0	0	0	0
d	1	0	0	0	-1	0	0	0	-1	0	1	1	0	0	0	0
f	0	0	0	0	0	0	-1	1	0	1	0	0	0	0	0	2
g	0	0	0	-1	0	-1	1	0	0	0	0	0	0	0	0	0
h	0	0	0	0	0	0	0	0	0	-1	-1	0	1	-1	0	0
j	0	0	0	0	0	0	0	0	0	0	0	-1	-1	0	2	0

	e_1	e_2	e_3	e_4	e_5	e_6	e_7	e_8	e_9	$e_{10}$ e_{10}	$e_{11}$ e_{11}	$e_{12}$ e_{12}	$e_{13}$ e_{13}	$e_{14}$ e_{14}	$e_{15}$ e_{15}	$e_{16}$ e_{16}
a	-1	1	1	0	0	0	0	0	1	0	0	0	0	0	0	0
b	0	0	-1	0	1	1	0	-1	0	0	0	0	0	1	0	0
c	0	-1	0	1	0	0	0	0	0	0	0	0	0	0	0	0
d	1	0	0	0	-1	0	0	0	-1	0	1	1	0	0	0	0
f	0	0	0	0	0	0	-1	1	0	1	0	0	0	0	0	2
g	0	0	0	-1	0	-1	1	0	0	0	0	0	0	0	0	0
h	0	0	0	0	0	0	0	0	0	-1	-1	0	1	-1	0	0
j	0	0	0	0	0	0	0	0	0	0	0	-1	-1	0	2	0

	e_1	e_2	e_3	e_4	e_5	e_6	e_7	e_8	e_9	$e_{10}$ e_{10}	$e_{11}$ e_{11}	$e_{12}$ e_{12}	$e_{13}$ e_{13}	$e_{14}$ e_{14}	$e_{15}$ e_{15}	$e_{16}$ e_{16}
a	-1	1	1	0	0	0	0	0	1	0	0	0	0	0	0	0
b	0	0	-1	0	1	1	0	-1	0	0	0	0	0	1	0	0
c	0	-1	0	1	0	0	0	0	0	0	0	0	0	0	0	0
d	1	0	0	0	-1	0	0	0	-1	0	-1	1	0	0	0	0
f	0	0	0	0	0	0	-1	1	0	1	0	0	0	0	0	2
g	0	0	0	-1	0	-1	1	0	0	0	0	0	0	0	0	0
h	0	0	0	0	0	0	0	0	0	-1	1	0	1	-1	0	0
j	0	0	0	0	0	0	0	0	0	0	0	-1	-1	0	2	0

	e_1	e_2	e_3	e_4	e_5	e_6	e_7	e_8	e_9	$e_{10}$ e_{10}	$e_{11}$ e_{11}	$e_{1 2}$ e_{1 2}	$e_{1 3}$ e_{1 3}	$e_{14}$ e_{14}	$e_{1 5}$ e_{1 5}	$e_{1 6}$ e_{1 6}
a	1	1	1	0	0	0	0	0	1	0	0	0	0	0	0	0
b	0	0	1	0	1	1	0	1	0	0	0	0	0	1	0	0
c	0	1	0	1	0	0	0	0	0	0	0	0	0	0	0	0
d	1	0	0	0	1	0	0	0	1	0	1	1	0	0	0	0
f	0	0	0	0	0	0	1	1	0	1	0	0	0	0	0	2
g	0	0	0	1	0	1	1	0	0	0	0	0	0	0	0	0
h	0	0	0	0	0	0	0	0	0	1	1	0	1	1	0	0
j	0	0	0	0	0	0	0	0	0	0	0	1	1	0	2	0

	e_1	e_2	e_3	e_4	e_5	e_6	e_7	e_8	e_9	$e_{10}$ e_{10}	$e_{11}$ e_{11}	$e_{1 2}$ e_{1 2}	$e_{1 3}$ e_{1 3}	$e_{14}$ e_{14}	$e_{1 5}$ e_{1 5}	$e_{1 6}$ e_{1 6}
a	1	1	1	0	0	0	0	0	1	0	0	0	0	0	0	0
b	0	0	0	0	1	1	0	1	0	0	0	0	0	1	0	0
c	0	1	0	1	0	0	0	0	0	0	0	0	0	0	0	0
d	1	0	0	0	1	0	0	0	1	0	1	1	0	0	0	0
f	0	0	1	0	0	0	1	1	0	1	0	0	0	0	0	2
g	0	0	0	1	0	1	1	0	0	0	0	0	0	0	0	0
h	0	0	0	0	0	0	0	0	0	1	1	0	1	1	0	0
j	0	0	0	0	0	0	0	0	0	0	0	1	1	0	2	0

	e_1	e_2	e_3	e_4	e_5	e_6	e_7	e_8	e_9	$e_{10}$ e_{10}	$e_{11}$ e_{11}	$e_{1 2}$ e_{1 2}	$e_{1 3}$ e_{1 3}	$e_{14}$ e_{14}	$e_{1 5}$ e_{1 5}	$e_{1 6}$ e_{1 6}
a	1	1	1	0	0	0	0	1	1	0	0	0	0	0	0	0
b	0	0	1	0	1	1	0	1	0	0	0	0	0	1	0	0
c	0	1	0	1	0	0	0	0	0	0	0	0	0	0	0	0
d	1	0	0	0	1	0	0	0	1	0	1	1	0	0	0	0
f	0	0	0	0	0	0	1	1	0	1	0	0	0	0	0	2
g	0	0	0	1	0	1	1	0	0	0	0	0	0	0	0	0
h	0	0	0	0	0	0	0	0	0	1	1	0	1	1	0	0
j	0	0	0	0	0	0	0	0	0	0	0	1	1	0	2	0

	a	b	c	d	f	g	h	j
a	0	1	1	1	0	0	0	0
b	0	0	0	1	0	2	1	0
c	0	0	0	0	0	1	0	0
d	1	0	0	1	0		1	1
f	0	1	0	0	0	1	1	0
g	1	0	0	0	2	0	0	0
h	0	0	0	0	1	0	0	1
j	0	0	0	0	0	0	2	1

	a	b	c	d	f	g	h	j
a	0	1	1	1	0	0	0	0
b	0	0	0	1	0	1	2	0
c	0	0	0	0	0	1	0	0
d	1	0	0	1	0	0	1	1
f	0	0	0	0	1	1	1	0
g	1	0	0	0	2	0	0	0
h	0	0	0	0	1	0	0	0
j	0	0	0	0	0	0	1	2

	a	b	c	d	f	g	h	j
a	0	1	1	1	0	0	0	0
b	0	0	0	1	0	1	2	0
c	0	0	0	0	0	1	0	0
d	1	0	0	1	0	0	1	1
f	0	1	0	0	1	1	1	0
g	1	0	0	0	2	0	0	0
h	0	0	0	0	1	0	0	1
j	0	0	0	0	0	0	2	1

	e_1	e_2	e_3	e_4	e_5	e_6	e_7	e_8	e_9	$e_{10}$ e_{10}	$e_{11}$ e_{11}	$e_{12}$ e_{12}	$e_{13}$ e_{13}	$e_{14}$ e_{14}	$e_{15}$ e_{15}	$e_{16}$ e_{16}
a	-1	1	1	0	0	0	0	0	1	0	0	0	0	0	0	0
b	0	0	-1	0	1	1	1	-1	0	0	0	0	0	1	0	0
c	0	-1	0	1	0	0	0	0	0	0	0	0	0	0	0	0
d	1	0	0	0	-1	0	0	0	-1	0	1	1	0	0	0	0
f	0	0	0	0	0	0	-1	1	0	1	0	0	0	0	0	2
g	0	0	0	-1	0	-1	1	0	0	0	0	0	0	0	0	0
h	0	0	0	0	0	0	0	0	0	-1	-1	0	1	-1	0	0
j	0	0	0	0	0	0	0	0	0	0	0	-1	-1	0	2	0

	e_1	e_2	e_3	e_4	e_5	e_6	e_7	e_8	e_9	$e_{10}$ e_{10}	$e_{11}$ e_{11}	$e_{12}$ e_{12}	$e_{13}$ e_{13}	$e_{14}$ e_{14}	$e_{15}$ e_{15}	$e_{16}$ e_{16}
a	-1	1	1	0	0	0	0	0	1	0	0	0	0	0	0	0
b	0	0	-1	0	1	1	0	-1	0	0	0	0	0	1	0	0
c	0	-1	0	1	0	0	0	0	0	0	0	0	0	0	0	0
d	1	0	0	0	-1	0	0	0	-1	0	1	1	0	0	0	0
f	0	0	0	0	0	0	-1	1	0	1	0	0	0	0	0	2
g	0	0	0	-1	0	-1	1	0	0	0	0	0	0	0	0	0
h	0	0	0	0	0	0	0	0	0	-1	-1	0	1	-1	0	0
j	0	0	0	0	0	0	0	0	0	0	0	-1	-1	0	2	0

	e_1	e_2	e_3	e_4	e_5	e_6	e_7	e_8	e_9	$e_{10}$ e_{10}	$e_{11}$ e_{11}	$e_{12}$ e_{12}	$e_{13}$ e_{13}	$e_{14}$ e_{14}	$e_{15}$ e_{15}	$e_{16}$ e_{16}
a	-1	1	1	0	0	0	0	0	1	0	0	0	0	0	0	0
b	0	0	-1	0	1	1	0	-1	0	0	0	0	0	1	0	0
c	0	-1	0	1	0	0	0	0	0	0	0	0	0	0	0	0
d	1	0	0	0	-1	0	0	0	-1	0	-1	1	0	0	0	0
f	0	0	0	0	0	0	-1	1	0	1	0	0	0	0	0	2
g	0	0	0	-1	0	-1	1	0	0	0	0	0	0	0	0	0
h	0	0	0	0	0	0	0	0	0	-1	1	0	1	-1	0	0
j	0	0	0	0	0	0	0	0	0	0	0	-1	-1	0	2	0

	e_1	e_2	e_3	e_4	e_5	e_6	e_7	e_8	e_9	$e_{10}$ e_{10}	$e_{11}$ e_{11}	$e_{1 2}$ e_{1 2}	$e_{1 3}$ e_{1 3}	$e_{14}$ e_{14}	$e_{1 5}$ e_{1 5}	$e_{1 6}$ e_{1 6}
a	1	1	1	0	0	0	0	0	1	0	0	0	0	0	0	0
b	0	0	1	0	1	1	0	1	0	0	0	0	0	1	0	0
c	0	1	0	1	0	0	0	0	0	0	0	0	0	0	0	0
d	1	0	0	0	1	0	0	0	1	0	1	1	0	0	0	0
f	0	0	0	0	0	0	1	1	0	1	0	0	0	0	0	2
g	0	0	0	1	0	1	1	0	0	0	0	0	0	0	0	0
h	0	0	0	0	0	0	0	0	0	1	1	0	1	1	0	0
j	0	0	0	0	0	0	0	0	0	0	0	1	1	0	2	0

	e_1	e_2	e_3	e_4	e_5	e_6	e_7	e_8	e_9	$e_{10}$ e_{10}	$e_{11}$ e_{11}	$e_{1 2}$ e_{1 2}	$e_{1 3}$ e_{1 3}	$e_{14}$ e_{14}	$e_{1 5}$ e_{1 5}	$e_{1 6}$ e_{1 6}
a	1	1	1	0	0	0	0	0	1	0	0	0	0	0	0	0
b	0	0	0	0	1	1	0	1	0	0	0	0	0	1	0	0
c	0	1	0	1	0	0	0	0	0	0	0	0	0	0	0	0
d	1	0	0	0	1	0	0	0	1	0	1	1	0	0	0	0
f	0	0	1	0	0	0	1	1	0	1	0	0	0	0	0	2
g	0	0	0	1	0	1	1	0	0	0	0	0	0	0	0	0
h	0	0	0	0	0	0	0	0	0	1	1	0	1	1	0	0
j	0	0	0	0	0	0	0	0	0	0	0	1	1	0	2	0

	e_1	e_2	e_3	e_4	e_5	e_6	e_7	e_8	e_9	$e_{10}$ e_{10}	$e_{11}$ e_{11}	$e_{1 2}$ e_{1 2}	$e_{1 3}$ e_{1 3}	$e_{14}$ e_{14}	$e_{1 5}$ e_{1 5}	$e_{1 6}$ e_{1 6}
a	1	1	1	0	0	0	0	1	1	0	0	0	0	0	0	0
b	0	0	1	0	1	1	0	1	0	0	0	0	0	1	0	0
c	0	1	0	1	0	0	0	0	0	0	0	0	0	0	0	0
d	1	0	0	0	1	0	0	0	1	0	1	1	0	0	0	0
f	0	0	0	0	0	0	1	1	0	1	0	0	0	0	0	2
g	0	0	0	1	0	1	1	0	0	0	0	0	0	0	0	0
h	0	0	0	0	0	0	0	0	0	1	1	0	1	1	0	0
j	0	0	0	0	0	0	0	0	0	0	0	1	1	0	2	0

	a	b	c	d	f	g	h	j
a	0	1	1	1	0	0	0	0
b	0	0	0	1	0	2	1	0
c	0	0	0	0	0	1	0	0
d	1	0	0	1	0		1	1
f	0	1	0	0	0	1	1	0
g	1	0	0	0	2	0	0	0
h	0	0	0	0	1	0	0	1
j	0	0	0	0	0	0	2	1

	a	b	c	d	f	g	h	j
a	0	1	1	1	0	0	0	0
b	0	0	0	1	0	1	2	0
c	0	0	0	0	0	1	0	0
d	1	0	0	1	0	0	1	1
f	0	0	0	0	1	1	1	0
g	1	0	0	0	2	0	0	0
h	0	0	0	0	1	0	0	0
j	0	0	0	0	0	0	1	2

	a	b	c	d	f	g	h	j
a	0	1	1	1	0	0	0	0
b	0	0	0	1	0	1	2	0
c	0	0	0	0	0	1	0	0
d	1	0	0	1	0	0	1	1
f	0	1	0	0	1	1	1	0
g	1	0	0	0	2	0	0	0
h	0	0	0	0	1	0	0	1
j	0	0	0	0	0	0	2	1

	e_1	e_2	e_3	e_4	e_5	e_6	e_7	e_8	e_9	$e_{10}$ e_{10}	$e_{11}$ e_{11}	$e_{12}$ e_{12}	$e_{13}$ e_{13}	$e_{14}$ e_{14}	$e_{15}$ e_{15}	$e_{16}$ e_{16}
a	-1	1	1	0	0	0	0	0	1	0	0	0	0	0	0	0
b	0	0	-1	0	1	1	1	-1	0	0	0	0	0	1	0	0
c	0	-1	0	1	0	0	0	0	0	0	0	0	0	0	0	0
d	1	0	0	0	-1	0	0	0	-1	0	1	1	0	0	0	0
f	0	0	0	0	0	0	-1	1	0	1	0	0	0	0	0	2
g	0	0	0	-1	0	-1	1	0	0	0	0	0	0	0	0	0
h	0	0	0	0	0	0	0	0	0	-1	-1	0	1	-1	0	0
j	0	0	0	0	0	0	0	0	0	0	0	-1	-1	0	2	0

	e_1	e_2	e_3	e_4	e_5	e_6	e_7	e_8	e_9	$e_{10}$ e_{10}	$e_{11}$ e_{11}	$e_{12}$ e_{12}	$e_{13}$ e_{13}	$e_{14}$ e_{14}	$e_{15}$ e_{15}	$e_{16}$ e_{16}
a	-1	1	1	0	0	0	0	0	1	0	0	0	0	0	0	0
b	0	0	-1	0	1	1	0	-1	0	0	0	0	0	1	0	0
c	0	-1	0	1	0	0	0	0	0	0	0	0	0	0	0	0
d	1	0	0	0	-1	0	0	0	-1	0	1	1	0	0	0	0
f	0	0	0	0	0	0	-1	1	0	1	0	0	0	0	0	2
g	0	0	0	-1	0	-1	1	0	0	0	0	0	0	0	0	0
h	0	0	0	0	0	0	0	0	0	-1	-1	0	1	-1	0	0
j	0	0	0	0	0	0	0	0	0	0	0	-1	-1	0	2	0

	e_1	e_2	e_3	e_4	e_5	e_6	e_7	e_8	e_9	$e_{10}$ e_{10}	$e_{11}$ e_{11}	$e_{12}$ e_{12}	$e_{13}$ e_{13}	$e_{14}$ e_{14}	$e_{15}$ e_{15}	$e_{16}$ e_{16}
a	-1	1	1	0	0	0	0	0	1	0	0	0	0	0	0	0
b	0	0	-1	0	1	1	0	-1	0	0	0	0	0	1	0	0
c	0	-1	0	1	0	0	0	0	0	0	0	0	0	0	0	0
d	1	0	0	0	-1	0	0	0	-1	0	-1	1	0	0	0	0
f	0	0	0	0	0	0	-1	1	0	1	0	0	0	0	0	2
g	0	0	0	-1	0	-1	1	0	0	0	0	0	0	0	0	0
h	0	0	0	0	0	0	0	0	0	-1	1	0	1	-1	0	0
j	0	0	0	0	0	0	0	0	0	0	0	-1	-1	0	2	0

	e_1	e_2	e_3	e_4	e_5	e_6	e_7	e_8	e_9	$e_{10}$ e_{10}	$e_{11}$ e_{11}	$e_{1 2}$ e_{1 2}	$e_{1 3}$ e_{1 3}	$e_{14}$ e_{14}	$e_{1 5}$ e_{1 5}	$e_{1 6}$ e_{1 6}
a	1	1	1	0	0	0	0	0	1	0	0	0	0	0	0	0
b	0	0	1	0	1	1	0	1	0	0	0	0	0	1	0	0
c	0	1	0	1	0	0	0	0	0	0	0	0	0	0	0	0
d	1	0	0	0	1	0	0	0	1	0	1	1	0	0	0	0
f	0	0	0	0	0	0	1	1	0	1	0	0	0	0	0	2
g	0	0	0	1	0	1	1	0	0	0	0	0	0	0	0	0
h	0	0	0	0	0	0	0	0	0	1	1	0	1	1	0	0
j	0	0	0	0	0	0	0	0	0	0	0	1	1	0	2	0

	e_1	e_2	e_3	e_4	e_5	e_6	e_7	e_8	e_9	$e_{10}$ e_{10}	$e_{11}$ e_{11}	$e_{1 2}$ e_{1 2}	$e_{1 3}$ e_{1 3}	$e_{14}$ e_{14}	$e_{1 5}$ e_{1 5}	$e_{1 6}$ e_{1 6}
a	1	1	1	0	0	0	0	0	1	0	0	0	0	0	0	0
b	0	0	0	0	1	1	0	1	0	0	0	0	0	1	0	0
c	0	1	0	1	0	0	0	0	0	0	0	0	0	0	0	0
d	1	0	0	0	1	0	0	0	1	0	1	1	0	0	0	0
f	0	0	1	0	0	0	1	1	0	1	0	0	0	0	0	2
g	0	0	0	1	0	1	1	0	0	0	0	0	0	0	0	0
h	0	0	0	0	0	0	0	0	0	1	1	0	1	1	0	0
j	0	0	0	0	0	0	0	0	0	0	0	1	1	0	2	0

	e_1	e_2	e_3	e_4	e_5	e_6	e_7	e_8	e_9	$e_{10}$ e_{10}	$e_{11}$ e_{11}	$e_{1 2}$ e_{1 2}	$e_{1 3}$ e_{1 3}	$e_{14}$ e_{14}	$e_{1 5}$ e_{1 5}	$e_{1 6}$ e_{1 6}
a	1	1	1	0	0	0	0	1	1	0	0	0	0	0	0	0
b	0	0	1	0	1	1	0	1	0	0	0	0	0	1	0	0
c	0	1	0	1	0	0	0	0	0	0	0	0	0	0	0	0
d	1	0	0	0	1	0	0	0	1	0	1	1	0	0	0	0
f	0	0	0	0	0	0	1	1	0	1	0	0	0	0	0	2
g	0	0	0	1	0	1	1	0	0	0	0	0	0	0	0	0
h	0	0	0	0	0	0	0	0	0	1	1	0	1	1	0	0
j	0	0	0	0	0	0	0	0	0	0	0	1	1	0	2	0