Re: Aufgaben und Übungen,

        b a x   b a y
0       0 0 0   1 1 1
1       0 0 1   0 1 0
2       0 1 0   0 0 0
3       0 1 1   1 1 1
4       1 0 0   0 1 0
5       1 0 1   1 0 1
6       1 1 0   1 1 1
7       1 1 1   0 1 0


        b a x   b
0       0 0 0   1
3       0 1 1   1
5       1 0 1   1
6       1 1 0   1

        b a x   a
0       0 0 0   1
1       0 0 1   1
3       0 1 1   1
4       1 0 0   1
6       1 1 0   1
7       1 1 1   1

        b a x   y
0       0 0 0   1
3       0 1 1   1
5       1 0 1   1
6       1 1 0   1



        b a x   b
Gruppe 0:
0       0 0 0   1
Gruppe 2:
3       0 1 1   1
5       1 0 1   1
6       1 1 0   1

        b a x   a
Gruppe 0:
0       0 0 0   1
Gruppe 1:
1       0 0 1   1
4       1 0 0   1
Gruppe 2:
3       0 1 1   1
6       1 1 0   1
Gruppe 3:
7       1 1 1   1

        b a x   y
Gruppe 0:
0       0 0 0   1
Gruppe 2:
3       0 1 1   1
5       1 0 1   1
6       1 1 0   1



        b a x   b
Gruppe 0:
0       0 0 0   1
Gruppe 2:
3       0 1 1   1
5       1 0 1   1
6       1 1 0   1

b := (not b and not and not x) or (not b and a and x) or (b and not a and x) or (b and a and not x)

        b a x   a
Gruppe 0:
0       0 0 0   1
Gruppe 1:
1       0 0 1   1
4       1 0 0   1
Gruppe 2:
3       0 1 1   1
6       1 1 0   1
Gruppe 3:
7       1 1 1   1

0;1     0 0 -
0;4     - 0 0
1;3     0 - 1
4;6     1 - 0
3;7     - 1 1
6;7     1 1 -

0;1     0 0 -
6;7     1 1 -
3;7     - 1 1
0;4     - 0 0
1;3     0 - 1
4;6     1 - 0

Gruppe 0:
0;1     0 0 -
Gruppe 2:
6;7     1 1 -
Gruppe 2:
3;7     - 1 1
Gruppe 0:
0;4     - 0 0
Gruppe 1:
1;3     0 - 1
Gruppe 1:
4;6     1 - 0

a := (not b and not a) or (b and a) or (a and x) or (not a and not x) or (not b and x) or (b and not x)


        b a x   y
Gruppe 0:
0       0 0 0   1
Gruppe 2:
3       0 1 1   1
5       1 0 1   1
6       1 1 0   1

y := (not b and not and not x) or (not b and a and x) or (b and not a and x) or (b and a and not x)


a := (not b and not a) or (b and a) or (a and x) or (not a and not x) or (not b and x) or (b and not x)

y := b := (not b and not and not x) or (not b and a and x) or (b and not a and x) or (b and a and not x)

        b a x   b a y
0       0 0 0   0 1 0
1       0 0 1   1 0 1
2       0 1 0   1 1 1
3       0 1 1   0 0 1
4       1 0 0   1 0 0
5       1 0 1   0 1 0
6       1 1 0   0 0 0
7       1 1 1   1 1 0


        b a x   b
0       0 0 0   0
1       0 0 1   1
2       0 1 0   1
3       0 1 1   0
4       1 0 0   1
5       1 0 1   0
6       1 1 0   0
7       1 1 1   1

        b a x   a
0       0 0 0   1
1       0 0 1   0
2       0 1 0   1
3       0 1 1   0
4       1 0 0   0
5       1 0 1   1
6       1 1 0   0
7       1 1 1   1

        b a x   y
0       0 0 0   0
1       0 0 1   1
2       0 1 0   1
3       0 1 1   1
4       1 0 0   0
5       1 0 1   0
6       1 1 0   0
7       1 1 1   0



        b a x   b
1       0 0 1   1
2       0 1 0   1
4       1 0 0   1
7       1 1 1   1

        b a x   a
0       0 0 0   1
2       0 1 0   1
5       1 0 1   1
7       1 1 1   1

        b a x   y
1       0 0 1   1
2       0 1 0   1
3       0 1 1   1



        b a x   b
Gruppe 1:
1       0 0 1   1
2       0 1 0   1
4       1 0 0   1
Gruppe 3:
7       1 1 1   1

        b a x   a
Gruppe 0:
0       0 0 0   1
Gruppe 1:
2       0 1 0   1
Gruppe 2:
5       1 0 1   1
Gruppe 3:
7       1 1 1   1

        b a x   y
Gruppe 1:
1       0 0 1   1
2       0 1 0   1
Gruppe 2:
3       0 1 1   1




        b a x   b
Gruppe 1:
1       0 0 1   1
2       0 1 0   1
4       1 0 0   1
Gruppe 3:
7       1 1 1   1

b := (not b and not a and x) or (not b and a and not x) or (b and not a and not x) or (b and a and x)

        b a x   a
Gruppe 0:
0       0 0 0   1
Gruppe 1:
2       0 1 0   1
Gruppe 2:
5       1 0 1   1
Gruppe 3:
7       1 1 1   1

0;2     0 - 0
5;7     1 - 1

a := (not b and not a) or (b and a)

        b a x   y
Gruppe 1:
1       0 0 1   1
2       0 1 0   1
Gruppe 2:
3       0 1 1   1

1;3     0 - 1
2;3     0 1 -

y := (not b and a) or (not b and x)


b := (not b and not a and x) or (not b and a and not x) or (b and not a and not x) or (b and a and x)
a := (not b and not a) or (b and a)
y := (not b and a) or (not b and x)

        b a x   b a y
0       0 0 0   1 1 1
1       0 0 1   0 1 0
2       0 1 0   1 1 0
3       0 1 1   0 0 1
4       1 0 0   1 0 1
5       1 0 1   1 1 0
6       1 1 0   1 0 1
7       1 1 1   0 1 0


        b a x   b
0       0 0 0   1
1       0 0 1   0
2       0 1 0   1
3       0 1 1   0
4       1 0 0   1
5       1 0 1   1
6       1 1 0   1
7       1 1 1   0

        b a x   a
0       0 0 0   1
1       0 0 1   1
2       0 1 0   1
3       0 1 1   0
4       1 0 0   0
5       1 0 1   1
6       1 1 0   0
7       1 1 1   1

        b a x   y
0       0 0 0   1
1       0 0 1   0
2       0 1 0   0
3       0 1 1   1
4       1 0 0   1
5       1 0 1   0
6       1 1 0   1
7       1 1 1   0



        b a x   b
0       0 0 0   1
2       0 1 0   1
4       1 0 0   1
5       1 0 1   1
6       1 1 0   1

        b a x   a
0       0 0 0   1
1       0 0 1   1
2       0 1 0   1
5       1 0 1   1
7       1 1 1   1

        b a x   y
0       0 0 0   1
3       0 1 1   1
4       1 0 0   1
6       1 1 0   1



        b a x   b
Gruppe 0:
0       0 0 0   1
Gruppe 1:
2       0 1 0   1
4       1 0 0   1
Gruppe 2:
5       1 0 1   1
6       1 1 0   1

        b a x   a
Gruppe 0:
0       0 0 0   1
Gruppe 1:
1       0 0 1   1
2       0 1 0   1
5       1 0 1   1
Gruppe 3:
7       1 1 1   1

        b a x   y
Gruppe 0:
0       0 0 0   1
Gruppe 1:
4       1 0 0   1
Gruppe 2:
3       0 1 1   1
6       1 1 0   1



        b a x   b
Gruppe 0:
0       0 0 0   1
Gruppe 1:
2       0 1 0   1
4       1 0 0   1
Gruppe 2:
5       1 0 1   1
6       1 1 0   1

0;2     0 - 1
0;4     - 0 0
4;6     1 - 0
4;5     1 0 -
1;6     - 1 0



0;4     - 0 0
1;6     - 1 0
0;2     0 - 1
4;6     1 - 0
4;5     1 0 -

0;4;1;6     - - 0
0;2         0 - 1
4;6         1 - 0
4;5         1 0 -

b <- (not x) or (not b and x) or (b and not x) or (b and not a)


        b a x   a
Gruppe 0:
0       0 0 0   1
Gruppe 1:
1       0 0 1   1
2       0 1 0   1
Gruppe 2:
5       1 0 1   1
Gruppe 3:
7       1 1 1   1


0;1     0 0 -
0;2     0 - 0
5;7     1 - 1

a <- (not b and not a) or (not b and not x) or (b and x)



        b a x   y
Gruppe 0:
0       0 0 0   1
Gruppe 1:
4       1 0 0   1
Gruppe 2:
3       0 1 1   1
6       1 1 0   1

0;4     - 0 0
3       0 1 1
4;6     1 - 0

y <- (not a and not x) or (not b and a and x) or (b and not x)


b <- (not x) or (not b and x) or (b and not x) or (b and not a)
a <- (not b and not a) or (not b and not x) or (b and x)
y <- (not a and not x) or (not b and a and x) or (b and not x)

        b a x   b a y
0       0 0 0   0 0 1
1       0 0 1   1 1 0
2       0 1 0   0 0 0
3       0 1 1   1 0 0
4       1 0 0   1 1 0
5       1 0 1   0 1 1
6       1 1 0   0 0 0
7       1 1 1   0 1 0


        b a x   b
0       0 0 0   0
1       0 0 1   1
2       0 1 0   0
3       0 1 1   1
4       1 0 0   1
5       1 0 1   0
6       1 1 0   0
7       1 1 1   0

        b a x   a
0       0 0 0   0
1       0 0 1   1
2       0 1 0   0
3       0 1 1   0
4       1 0 0   1
5       1 0 1   1
6       1 1 0   0
7       1 1 1   1

        b a x   y
0       0 0 0   1
1       0 0 1   0
2       0 1 0   0
3       0 1 1   0
4       1 0 0   0
5       1 0 1   1
6       1 1 0   0
7       1 1 1   0




        b a x   b
1       0 0 1   1
3       0 1 1   1
4       1 0 0   1

        b a x   a
1       0 0 1   1
4       1 0 0   1
5       1 0 1   1
7       1 1 1   1

        b a x   y
0       0 0 0   1
5       1 0 1   1



        b a x   b
1       0 0 1   1
3       0 1 1   1
4       1 0 0   1

        b a x   a
1       0 0 1   1
4       1 0 0   1
5       1 0 1   1
7       1 1 1   1

        b a x   y
0       0 0 0   1
5       1 0 1   1



        b a x   b
1       0 0 1   1
3       0 1 1   1
4       1 0 0   1

        b a x   a
1       0 0 1   1
4       1 0 0   1
5       1 0 1   1
7       1 1 1   1

        b a x   y
0       0 0 0   1
5       1 0 1   1



        b a x   b
Gruppe 1:
1       0 0 1   1
4       1 0 0   1
Gruppe 2:
3       0 1 1   1

        b a x   a
Gruppe 1:
1       0 0 1   1
4       1 0 0   1
Gruppe 2:
5       1 0 1   1
Gruppe 3:
7       1 1 1   1

        b a x   y
Gruppe 0:
0       0 0 0   1
Gruppe 2:
5       1 0 1   1



        b a x   b
Gruppe 1:
1       0 0 1   1
4       1 0 0   1
Gruppe 2:
3       0 1 1   1

1;3     0 - 1
4       1 0 0

b <- (not b and x) or (b and not a and not x)

        b a x   a
Gruppe 1:
1       0 0 1   1
4       1 0 0   1
Gruppe 2:
5       1 0 1   1
Gruppe 3:
7       1 1 1   1

1;4     - 0 1
4;5     1 0 -
5;7     1 - 1

a <- (not a and x) or (b and not a) or (b and x)


        b a x   y
Gruppe 0:
0       0 0 0   1
Gruppe 2:
5       1 0 1   1

y <- (not b and not a and not x) or (b and not a and x)


b <- (not b and x) or (b and not a and not x)
a <- (not a and x) or (b and not a) or (b and x)
y <- (not b and not a and not x) or (b and not a and x)

        b a x   b a y
0       0 0 0   0 1 0
1       0 0 1   1 0 0
2       0 1 0   0 1 1
3       0 1 1   0 0 1
4       1 0 0   1 1 0
5       1 0 1   0 1 0
6       1 1 0   0 0 1
7       1 1 1   1 1 0


        b a x   b
0       0 0 0   0
1       0 0 1   1
2       0 1 0   0
3       0 1 1   0
4       1 0 0   1
5       1 0 1   0
6       1 1 0   0
7       1 1 1   1

        b a x   a
0       0 0 0   1
1       0 0 1   0
2       0 1 0   1
3       0 1 1   0
4       1 0 0   1
5       1 0 1   1
6       1 1 0   0
7       1 1 1   1

        b a x   y
0       0 0 0   0
1       0 0 1   0
2       0 1 0   1
3       0 1 1   1
4       1 0 0   0
5       1 0 1   0
6       1 1 0   1
7       1 1 1   0




        b a x   b
1       0 0 1   1
4       1 0 0   1
7       1 1 1   1

        b a x   a
0       0 0 0   1
2       0 1 0   1
4       1 0 0   1
5       1 0 1   1
7       1 1 1   1

        b a x   y
2       0 1 0   1
3       0 1 1   1
6       1 1 0   1



        b a x   b
Gruppe 1:
1       0 0 1   1
4       1 0 0   1
Gruppe 3:
7       1 1 1   1

        b a x   a
Gruppe 0:
0       0 0 0   1
Gruppe 1:
2       0 1 0   1
4       1 0 0   1
Gruppe 2:
5       1 0 1   1
Gruppe 3:
7       1 1 1   1

        b a x   y
Gruppe 1:
2       0 1 0   1
Gruppe 2:
3       0 1 1   1
6       1 1 0   1



        b a x   b
Gruppe 1:
1       0 0 1   1
4       1 0 0   1
Gruppe 3:
7       1 1 1   1

1       0 0 1
4       1 0 0
7       1 1 1

b <- (not b and not a and x) or (b and not a and not x) or (b and a and x)

        b a x   a
Gruppe 0:
0       0 0 0   1
Gruppe 1:
2       0 1 0   1
4       1 0 0   1
Gruppe 2:
5       1 0 1   1
Gruppe 3:
7       1 1 1   1

0;2     0 - 0
0;4     - 0 0
4;5     1 0 -
5;7     1 - 1


0;4     - 0 0
5;7     1 - 1
0;2     0 - 0
4;5     1 0 -

a <- (not a and not x) or (b and x) or (not b and not x) or (b and not a)


        b a x   y
Gruppe 1:
2       0 1 0   1
Gruppe 2:
3       0 1 1   1
6       1 1 0   1

2;3     0 1 -
2;6     - 1 0

y <- (not b and a) or (a and not x)


b <- (not b and not a and x) or (b and not a and not x) or (b and a and x)
a <- (not a and not x) or (b and x) or (not b and not x) or (b and not a)
y <- (not b and a) or (a and not x)

        b a x   b a y
0       0 0 0   0 1 0
1       0 0 1   1 0 1
2       0 1 0   1 1 1
3       0 1 1   1 0 0
4       1 0 0   1 1 0
5       1 0 1   1 0 0
6       1 1 0   0 0 1
7       1 1 1   1 1 0


        b a x   b
0       0 0 0   0
1       0 0 1   1
2       0 1 0   1
3       0 1 1   1
4       1 0 0   1
5       1 0 1   1
6       1 1 0   0
7       1 1 1   1

        b a x   a
0       0 0 0   1
1       0 0 1   0
2       0 1 0   1
3       0 1 1   0
4       1 0 0   1
5       1 0 1   0
6       1 1 0   0
7       1 1 1   1

        b a x   y
0       0 0 0   0
1       0 0 1   1
2       0 1 0   1
3       0 1 1   0
4       1 0 0   0
5       1 0 1   0
6       1 1 0   1
7       1 1 1   0



        b a x   b
1       0 0 1   1
2       0 1 0   1
3       0 1 1   1
4       1 0 0   1
5       1 0 1   1
7       1 1 1   1

        b a x   a
0       0 0 0   1
2       0 1 0   1
4       1 0 0   1
7       1 1 1   1

        b a x   y
1       0 0 1   1
2       0 1 0   1
6       1 1 0   1



        b a x   b
Gruppe 1:
1       0 0 1   1
2       0 1 0   1
4       1 0 0   1
Gruppe 2:
3       0 1 1   1
5       1 0 1   1
Gruppe 3:
7       1 1 1   1

        b a x   a
Gruppe 0:
0       0 0 0   1
Gruppe 1:
2       0 1 0   1
4       1 0 0   1
Gruppe 3:
7       1 1 1   1

        b a x   y
Gruppe 1:
1       0 0 1   1
2       0 1 0   1
Gruppe 2:
6       1 1 0   1



        b a x   b
Gruppe 1:
1       0 0 1   1
2       0 1 0   1
4       1 0 0   1
Gruppe 2:
3       0 1 1   1
5       1 0 1   1
Gruppe 3:
7       1 1 1   1

1:3     0 - 1
2;3     0 1 -
1;5     - 0 1
4;5     1 0 -
3;7     - 1 1
5;7     1 - 1


1:3     0 - 1
5;7     1 - 1
2;3     0 1 -
4;5     1 0 -
1;5     - 0 1
3;7     - 1 1

1;3;5;7     - - 1
2;3         0 1 -
4;5         1 0 -

b <- not x or (not b and a) or (b and not a)

        b a x   a
Gruppe 0:
0       0 0 0   1
Gruppe 1:
2       0 1 0   1
4       1 0 0   1
Gruppe 3:
7       1 1 1   1

0;2     0 - 0
0;4     - 0 0
7       1 1 1

a <- (not b and not x) or (not a and not x) or (b and a and x)

        b a x   y
Gruppe 1:
1       0 0 1   1
2       0 1 0   1
Gruppe 2:
6       1 1 0   1
.
1       0 0 1
2;6     - 1 0


b <- not x or (not b and a) or (b and not a)
a <- (not b and not x) or (not a and not x) or (b and a and x)
y <- (not b and not a and x) or (a and not x)

        b a x   b a y
0       0 0 0   0 1 0
1       0 0 1   0 0 1
2       0 1 0   0 1 1
3       0 1 1   0 0 1
4       1 0 0   1 0 1
5       1 0 1   1 1 1
6       1 1 0   1 0 1
7       1 1 1   1 1 0


        b a x   b
0       0 0 0   0
1       0 0 1   0
2       0 1 0   0
3       0 1 1   0
4       1 0 0   1
5       1 0 1   1
6       1 1 0   1
7       1 1 1   1

        b a x   a
0       0 0 0   1
1       0 0 1   0
2       0 1 0   1
3       0 1 1   0
4       1 0 0   0
5       1 0 1   1
6       1 1 0   0
7       1 1 1   1

        b a x   y
0       0 0 0   0
1       0 0 1   1
2       0 1 0   1
3       0 1 1   1
4       1 0 0   1
5       1 0 1   1
6       1 1 0   1
7       1 1 1   0



        b a x   b
4       1 0 0   1
5       1 0 1   1
6       1 1 0   1
7       1 1 1   1

        b a x   a
0       0 0 0   1
2       0 1 0   1
5       1 0 1   1
7       1 1 1   1

        b a x   y
1       0 0 1   1
2       0 1 0   1
3       0 1 1   1
4       1 0 0   1
5       1 0 1   1
6       1 1 0   1



        b a x   b
Gruppe 1:
4       1 0 0   1
Gruppe 2:
5       1 0 1   1
6       1 1 0   1
Gruppe 3:
7       1 1 1   1

        b a x   a
Gruppe 0:
0       0 0 0   1
Gruppe 1:
2       0 1 0   1
Gruppe 2:
5       1 0 1   1
Gruppe 3:
7       1 1 1   1

        b a x   y
Gruppe 1:
1       0 0 1   1
2       0 1 0   1
4       1 0 0   1
Gruppe 2:
3       0 1 1   1
5       1 0 1   1
6       1 1 0   1


        b a x   b
Gruppe 1:
4       1 0 0   1
Gruppe 2:
5       1 0 1   1
6       1 1 0   1
Gruppe 3:
7       1 1 1   1

4;5     1 0 -
5;7     1 - 1
6;7     1 1 -

        4   5   6   7
4;5     *   *
5;7         *       *
6;7             *   *

        4   5   6   7
4;5     *   *
6;7             *   *

4;5;6;7  1 - -

b <- b

        b a x   a
Gruppe 0:
0       0 0 0   1
Gruppe 1:
2       0 1 0   1
Gruppe 2:
5       1 0 1   1
Gruppe 3:
7       1 1 1   1

0;2     0 - 0
5;7     1 - 1

a <- (not b and not x) or (b and x)

        b a x   y
Gruppe 1:
1       0 0 1   1
2       0 1 0   1
4       1 0 0   1
Gruppe 2:
3       0 1 1   1
5       1 0 1   1
6       1 1 0   1


1;3     0 - 1
1;2     - 0 1
2;3     0 - 1
2;6     - 1 0
4;5     1 0 -
4;6     1 - 0


1;3     0 - 1
4;6     1 - 0
1;2     - 0 1
2;6     - 1 0
2;3     0 1 -
4;5     1 0 -

        1   2   3   4   5   6
1;3     *       *
4;6                 *       *
1;2     *   *
2;6         *               *
2;3         *   *
4;5                 *   *


        1   2   3   4   5   6
1;3     *       *
4;6                 *       *
2;3         *   *
4;5                 *   *

y <- (not b and x) or (b and not x) or (not b and a) or (b and not a)


b <- b
a <- (not b and not x) or (b and x)
y <- (not b and x) or (b and not x) or (not b and a) or (b and not a)

        b a x   b a y
0       0 0 0   0 1 0
1       0 0 1   1 0 0
2       0 1 0   0 1 1
3       0 1 1   1 0 0
4       1 0 0   1 1 1
5       1 0 1   0 0 0
6       1 1 0   0 1 0
7       1 1 1   1 1 1


        b a x   b
0       0 0 0   0
1       0 0 1   1
2       0 1 0   0
3       0 1 1   1
4       1 0 0   1
5       1 0 1   0
6       1 1 0   0
7       1 1 1   1

        b a x   a
0       0 0 0   1
1       0 0 1   0
2       0 1 0   1
3       0 1 1   0
4       1 0 0   1
5       1 0 1   0
6       1 1 0   1
7       1 1 1   1

        b a x   y
0       0 0 0   0
1       0 0 1   0
2       0 1 0   1
3       0 1 1   0
4       1 0 0   1
5       1 0 1   0
6       1 1 0   0
7       1 1 1   1




        b a x   b
1       0 0 1   1
3       0 1 1   1
4       1 0 0   1
7       1 1 1   1

        b a x   a
0       0 0 0   1
2       0 1 0   1
4       1 0 0   1
6       1 1 0   1
7       1 1 1   1

        b a x   y
2       0 1 0   1
4       1 0 0   1
7       1 1 1   1



        b a x   b
Gruppe 1:
1       0 0 1   1
4       1 0 0   1
Gruppe 2:
3       0 1 1   1
Gruppe 3:
7       1 1 1   1

        b a x   a
Gruppe 0:
0       0 0 0   1
Gruppe 1:
2       0 1 0   1
4       1 0 0   1
Gruppe 2:
6       1 1 0   1
Gruppe 3:
7       1 1 1   1

        b a x   y
Gruppe 1:
2       0 1 0   1
4       1 0 0   1
Gruppe 3:
7       1 1 1   1



        b a x   b
Gruppe 1:
1       0 0 1   1
4       1 0 0   1
Gruppe 2:
3       0 1 1   1
Gruppe 3:
7       1 1 1   1

1;3     0 - 1
4       1 0 0
3;7     - 1 1

b <- (not b and x) or (b and not a and not x) or (a and x)

        b a x   a
Gruppe 0:
0       0 0 0   1
Gruppe 1:
2       0 1 0   1
4       1 0 0   1
Gruppe 2:
6       1 1 0   1
Gruppe 3:
7       1 1 1   1

0;2     0 - 0
0;4     - 0 0
2;6     - 1 0
4;6     1 - 0
6;7     1 1 -

0;2     0 - 0
4;6     1 - 0
0;4     - 0 0
2;6     - 1 0
6;7     1 1 -

0;2;4;6     - - 0
0;4;2;6     - - 0
6;7         1 1 -

a <- (not x) or (b and a)

        b a x   y
Gruppe 1:
2       0 1 0   1
4       1 0 0   1
Gruppe 3:
7       1 1 1   1

y <- (not b and a and not x) or (b and not a and not x) or (b and a and x)



b <- (not b and x) or (b and not a and not x) or (a and x)
a <- (not x) or (b and a)
y <- (not b and a and not x) or (b and not a and not x) or (b and a and x)

        b a x   b a y
0       0 0 0   0 1 1
1       0 0 1   0 0 0
2       0 1 0   0 1 1
3       0 1 1   0 0 1
4       1 0 0   0 1 0
5       1 0 1   1 1 0
6       1 1 0   0 1 0
7       1 1 1   1 1 1


        b a x   b
0       0 0 0   0
1       0 0 1   0
2       0 1 0   0
3       0 1 1   0
4       1 0 0   0
5       1 0 1   1
6       1 1 0   0
7       1 1 1   1

        b a x   a
0       0 0 0   1
1       0 0 1   0
2       0 1 0   1
3       0 1 1   0
4       1 0 0   1
5       1 0 1   1
6       1 1 0   1
7       1 1 1   1

        b a x   y
0       0 0 0   1
1       0 0 1   0
2       0 1 0   1
3       0 1 1   1
4       1 0 0   0
5       1 0 1   0
6       1 1 0   0
7       1 1 1   1



        b a x   b
5       1 0 1   1
7       1 1 1   1

        b a x   a
0       0 0 0   1
2       0 1 0   1
4       1 0 0   1
5       1 0 1   1
6       1 1 0   1
7       1 1 1   1

        b a x   y
0       0 0 0   1
2       0 1 0   1
3       0 1 1   1
7       1 1 1   1



        b a x   b
Gruppe 2:
5       1 0 1   1
Gruppe 3:
7       1 1 1   1

        b a x   a
Gruppe 0:
0       0 0 0   1
Gruppe 1:
2       0 1 0   1
4       1 0 0   1
Gruppe 2:
5       1 0 1   1
6       1 1 0   1
Gruppe 3:
7       1 1 1   1

        b a x   y
Gruppe 0:
0       0 0 0   1
Gruppe 1:
2       0 1 0   1
Gruppe 2:
3       0 1 1   1
Gruppe 3:
7       1 1 1   1



        b a x   b
Gruppe 2:
5       1 0 1   1
Gruppe 3:
7       1 1 1   1

5;7     1 - 1

b <- (b and x)

        b a x   a
Gruppe 0:
0       0 0 0   1
Gruppe 1:
2       0 1 0   1
4       1 0 0   1
Gruppe 2:
5       1 0 1   1
6       1 1 0   1
Gruppe 3:
7       1 1 1   1

0;2     0 - 0
0;4     - 0 0
4;5     1 0 -
4;6     1 - 0
2;6     - 1 0
6;7     1 1 -
5;7     1 - 1

Gruppe 0:
0;2     0 - 0
Gruppe 1:
4;6     1 - 0
Gruppe 2:
5;7     1 - 1

0;2;4;6     - - 0
4;6;5;7     1 - -

0;4     - 0 0
2;6     - 1 0

0;4;2;6     - - 0

4;5     1 0 -
6;7     1 1 -

4;5;6;7 1 - -

0;2;4;6     - - 0
4;5;6;7     1 - -

a <- (not x or b)


        b a x   y
Gruppe 0:
0       0 0 0   1
Gruppe 1:
2       0 1 0   1
Gruppe 2:
3       0 1 1   1
Gruppe 3:
7       1 1 1   1

0;2     0 - 0
2;3     0 1 -
3;7     - 1 1

y <- (not b and not x) or (not b and a) or (a and x)



b <- (b and x)
a <- (not x or b)
y <- (not b and not x) or (not b and a) or (a and x)

        b a x   b a y
0       0 0 0   0 0 0
1       0 0 1   1 1 0
2       0 1 0   0 1 0
3       0 1 1   1 0 0
4       1 0 0   0 0 1
5       1 0 1   0 1 1
6       1 1 0   1 0 1
7       1 1 1   0 0 0


        b a x   b
0       0 0 0   0
1       0 0 1   1
2       0 1 0   0
3       0 1 1   1
4       1 0 0   0
5       1 0 1   0
6       1 1 0   1
7       1 1 1   0

        b a x   a
0       0 0 0   0
1       0 0 1   1
2       0 1 0   1
3       0 1 1   0
4       1 0 0   0
5       1 0 1   1
6       1 1 0   0
7       1 1 1   0

        b a x   y
0       0 0 0   0
1       0 0 1   0
2       0 1 0   0
3       0 1 1   0
4       1 0 0   1
5       1 0 1   1
6       1 1 0   1
7       1 1 1   0



        b a x   b
1       0 0 1   1
3       0 1 1   1
6       1 1 0   1

        b a x   a
1       0 0 1   1
2       0 1 0   1
5       1 0 1   1

        b a x   y
4       1 0 0   1
5       1 0 1   1
6       1 1 0   1



        b a x   b
Gruppe 1:
1       0 0 1   1
Gruppe 2:
3       0 1 1   1
6       1 1 0   1

        b a x   a
Gruppe 1:
1       0 0 1   1
2       0 1 0   1
Gruppe 2:
5       1 0 1   1

        b a x   y
Gruppe 1:
4       1 0 0   1
5       1 0 1   1
Gruppe 2:
6       1 1 0   1



        b a x   b
Gruppe 1:
1       0 0 1   1
Gruppe 2:
3       0 1 1   1
6       1 1 0   1

1;3     0 - 1
6       1 1 0

b <- (not b and x) or (b and a and not x)

        b a x   a
Gruppe 1:
1       0 0 1   1
2       0 1 0   1
Gruppe 2:
5       1 0 1   1

1;5     - 0 1
2       0 1 0

a <- (not a and x) or (not b and a and not x)

        b a x   y
Gruppe 1:
4       1 0 0   1
Gruppe 2:
5       1 0 1   1
6       1 1 0   1

4;5     1 0 -
4;6     1 - 0

y <- (b and not a) or (b and not x)


b <- (not b and x) or (b and a and not x)
a <- (not a and x) or (not b and a and not x)
y <- (b and not a) or (b and not x)

        b a x   b a y
0       0 0 0   0 1 1
1       0 0 1   0 0 1
2       0 1 0   0 1 1
3       0 1 1   1 1 1
4       1 0 0   1 0 0
5       1 0 1   0 0 1
6       1 1 0   1 0 1
7       1 1 1   0 1 1


        b a x   b
0       0 0 0   0
1       0 0 1   0
2       0 1 0   0
3       0 1 1   1
4       1 0 0   1
5       1 0 1   0
6       1 1 0   1
7       1 1 1   0

        b a x   a
0       0 0 0   1
1       0 0 1   0
2       0 1 0   1
3       0 1 1   1
4       1 0 0   0
5       1 0 1   0
6       1 1 0   0
7       1 1 1   1

        b a x   y
0       0 0 0   1
1       0 0 1   1
2       0 1 0   1
3       0 1 1   1
4       1 0 0   0
5       1 0 1   1
6       1 1 0   1
7       1 1 1   1



        b a x   b
3       0 1 1   1
4       1 0 0   1
6       1 1 0   1

        b a x   a
0       0 0 0   1
2       0 1 0   1
3       0 1 1   1
7       1 1 1   1

        b a x   y
0       0 0 0   1
1       0 0 1   1
2       0 1 0   1
3       0 1 1   1
5       1 0 1   1
6       1 1 0   1
7       1 1 1   1



        b a x   b
Gruppe 1:
4       1 0 0   1
Gruppe 2:
3       0 1 1   1
6       1 1 0   1

        b a x   a
Gruppe 0:
0       0 0 0   1
Gruppe 1:
2       0 1 0   1
Gruppe 2:
3       0 1 1   1
Gruppe 3:
7       1 1 1   1

        b a x   y
Gruppe 0:
0       0 0 0   1
Gruppe 1:
1       0 0 1   1
2       0 1 0   1
Gruppe 2:
3       0 1 1   1
5       1 0 1   1
6       1 1 0   1
Gruppe 3:
7       1 1 1   1



        b a x   b
Gruppe 1:
4       1 0 0   1
Gruppe 2:
3       0 1 1   1
6       1 1 0   1

4;6     1 - 0
3       0 1 1

b <- (b and not x) or (not b and a and x)

        b a x   a
Gruppe 0:
0       0 0 0   1
Gruppe 1:
2       0 1 0   1
Gruppe 2:
3       0 1 1   1
Gruppe 3:
7       1 1 1   1

0;2     0 - 0
2;3     0 1 -
3;7     - 1 1

a <- (not b and not x) or (a and x)


        b a x   y
Gruppe 0:
0       0 0 0   1
Gruppe 1:
1       0 0 1   1
2       0 1 0   1
Gruppe 2:
3       0 1 1   1
5       1 0 1   1
6       1 1 0   1
Gruppe 3:
7       1 1 1   1


0;1     0 0 -
0;2     0 - 0
1;3     0 - 1
1;5     - 0 1
2;3     0 1 -
2;6     - 1 0
3;7     - 1 1
5;7     1 - 1
6;7     1 1 -


1;5     - 0 1
2;6     - 1 0
3;7     - 1 1
0;2     0 - 0
1;3     0 - 1
5;7     1 - 1
0;1     0 0 -
2;3     0 1 -
6;7     1 1 -

1;5;3;7     - - 1
2;6;3;7     - 1 -
0;2;1;3     0 - -
1;3;5;7     - - 1
0;1;2;3     0 - -
2;3;6;7     - 1 -


1;5;3;7     - - 1
2;6;3;7     - 1 -
0;2;1;3     0 - -

y <- (x or a or not b)



b <- (b and not x) or (not b and a and x)
a <- (not b and not x) or (a and x)
y <- (x or a or not b)

        b a x   b a y
0       0 0 0   1 0 1
1       0 0 1   1 1 1
2       0 1 0   0 0 0
3       0 1 1   1 0 1
4       1 0 0   1 1 1
5       1 0 1   0 1 0
6       1 1 0   0 0 0
7       1 1 1   0 1 1


        b a x   b
0       0 0 0   1
1       0 0 1   1
2       0 1 0   0
3       0 1 1   1
4       1 0 0   1
5       1 0 1   0
6       1 1 0   0
7       1 1 1   0

        b a x   a
0       0 0 0   0
1       0 0 1   1
2       0 1 0   0
3       0 1 1   0
4       1 0 0   1
5       1 0 1   1
6       1 1 0   0
7       1 1 1   1

        b a x   y
0       0 0 0   1
1       0 0 1   1
2       0 1 0   0
3       0 1 1   1
4       1 0 0   1
5       1 0 1   0
6       1 1 0   0
7       1 1 1   1



        b a x   b
0       0 0 0   1
1       0 0 1   1
3       0 1 1   1
4       1 0 0   1

        b a x   a
1       0 0 1   1
4       1 0 0   1
5       1 0 1   1
7       1 1 1   1

        b a x   y
0       0 0 0   1
1       0 0 1   1
3       0 1 1   1
4       1 0 0   1
7       1 1 1   1



        b a x   b
Gruppe 0:
0       0 0 0   1
Gruppe 1:
1       0 0 1   1
4       1 0 0   1
Gruppe 2:
3       0 1 1   1


        b a x   a
Gruppe 1:
1       0 0 1   1
4       1 0 0   1
Gruppe 2:
5       1 0 1   1
Gruppe 3:
7       1 1 1   1

        b a x   y
Gruppe 0:
0       0 0 0   1
Gruppe 1:
1       0 0 1   1
4       1 0 0   1
Gruppe 2:
3       0 1 1   1
Gruppe 3:
7       1 1 1   1



        b a x   b
Gruppe 0:
0       0 0 0   1
Gruppe 1:
1       0 0 1   1
4       1 0 0   1
Gruppe 2:
3       0 1 1   1

0;1     0 0 -
0;4     - 0 0
1;3     0 - 1

        0   1   3   4
0;1     *   *
0;4     *           *
1;3         *   *

        0   1   3   4
0;4     *           *
1;3         *   *

b <- (not a and not x) or (not b and x)

        b a x   a
Gruppe 1:
1       0 0 1   1
4       1 0 0   1
Gruppe 2:
5       1 0 1   1
Gruppe 3:
7       1 1 1   1

1;5     - 0 1
4;5     1 0 -
5;7     1 - 1

        1   4   5   7
1;5     *       *
4;5         *   *
5;7             *   *

a <- (not a and x) or (b and not a) or (b and x)

        b a x   y
Gruppe 0:
0       0 0 0   1
Gruppe 1:
1       0 0 1   1
4       1 0 0   1
Gruppe 2:
3       0 1 1   1
Gruppe 3:
7       1 1 1   1

0;1     0 0 -
0;4     - 0 0
1;3     0 - 1
3;7     - 1 1

0;1     0 0 -
0;4     - 0 0
3;7     - 1 1
1;3     0 - 1

        0   1   3   4   7
0;1     *   *
0;4     *           *
3;7             *       *
1;3         *   *

        0   1   3   4   7
0;1     *   *
0;4     *           *
3;7             *       *

y <- (not b and not a) or (not a and not x) or (a and x)



b <- (not a and not x) or (not b and x)
a <- (not a and x) or (b and not a) or (b and x)
y <- (not b and not a) or (not a and not x) or (a and x)

        b a x   b a y
0       0 0 0   1 0 1
1       0 0 1   0 1 1
2       0 1 0   1 1 1
3       0 1 1   1 0 1
4       1 0 0   0 0 1
5       1 0 1   1 1 0
6       1 1 0   0 0 0
7       1 1 1   1 1 1


        b a x   b
0       0 0 0   1
1       0 0 1   0
2       0 1 0   1
3       0 1 1   1
4       1 0 0   0
5       1 0 1   1
6       1 1 0   0
7       1 1 1   1

        b a x   a
0       0 0 0   0
1       0 0 1   1
2       0 1 0   1
3       0 1 1   0
4       1 0 0   0
5       1 0 1   1
6       1 1 0   0
7       1 1 1   1

        b a x   y
0       0 0 0   1
1       0 0 1   1
2       0 1 0   1
3       0 1 1   1
4       1 0 0   1
5       1 0 1   0
6       1 1 0   0
7       1 1 1   1



        b a x   b
0       0 0 0   1
2       0 1 0   1
3       0 1 1   1
5       1 0 1   1
7       1 1 1   1

        b a x   a
1       0 0 1   1
2       0 1 0   1
5       1 0 1   1
7       1 1 1   1

        b a x   y
0       0 0 0   1
1       0 0 1   1
2       0 1 0   1
3       0 1 1   1
4       1 0 0   1
7       1 1 1   1



        b a x   b
Gruppe 0:
0       0 0 0   1
Gruppe 1:
2       0 1 0   1
Gruppe 2:
3       0 1 1   1
5       1 0 1   1
Gruppe 3:
7       1 1 1   1

3;7     - 1 1
0;2     0 - 0
5;7     1 - 1
2;3     0 1 -

        0   2   3   5   7
3;7             *       *
0;2     *   *
5;7                 *   *
2;3         *   *

        0   2   3   5   7
3;7             *       *
0;2     *   *
5;7                 *   *

b <- (a and x) or (not b and not x) or (b and x)

        b a x   a
Gruppe 1:
1       0 0 1   1
2       0 1 0   1
Gruppe 2:
5       1 0 1   1
Gruppe 3:
7       1 1 1   1

1;5     - 0 1
2       0 1 0
5;7     1 - 1

        1   2   5   7
1;5     *       *
2           *
5;7             *   *

a <- (not a and x) or (not b and a and not x) or (b and x)

        b a x   y
Gruppe 0:
0       0 0 0   1
Gruppe 1:
1       0 0 1   1
2       0 1 0   1
4       1 0 0   1
Gruppe 2:
3       0 1 1   1
Gruppe 3:
7       1 1 1   1

0;1     0 0 -
0;2     0 - 1
0;4     - 0 0
1;3     0 - 1
2;3     0 1 -
3;7     - 1 1


0;1     0 0 -
2;3     0 1 -
0;2     0 - 0
1;3     0 - 1
0;4     - 0 0
3;7     - 1 1

0;1;2;3     0 - -
0;2;1;3     0 - -
0;4         - 0 0
3;7         - 1 1

0;1;2;3     0 - -
0;4         - 0 0
3;7         - 1 1

y <- (not b) or (not a and not x) or (a and x)


b <- (a and x) or (not b and not x) or (b and x)
a <- (not a and x) or (not b and a and not x) or (b and x)
y <- (not b) or (not a and not x) or (a and x)

        b a x   b a y
0       0 0 0   0 0 1
1       0 0 1   0 1 0
2       0 1 0   1 1 1
3       0 1 1   0 0 1
4       1 0 0   1 0 1
5       1 0 1   0 0 0
6       1 1 0   1 0 1
7       1 1 1   1 1 1


        b a x   b
0       0 0 0   0
1       0 0 1   0
2       0 1 0   1
3       0 1 1   0
4       1 0 0   1
5       1 0 1   0
6       1 1 0   1
7       1 1 1   1

        b a x   a
0       0 0 0   0
1       0 0 1   1
2       0 1 0   1
3       0 1 1   0
4       1 0 0   0
5       1 0 1   0
6       1 1 0   0
7       1 1 1   1

        b a x   y
0       0 0 0   1
1       0 0 1   0
2       0 1 0   1
3       0 1 1   1
4       1 0 0   1
5       1 0 1   0
6       1 1 0   1
7       1 1 1   1



        b a x   b
2       0 1 0   1
4       1 0 0   1
6       1 1 0   1
7       1 1 1   1

        b a x   a
1       0 0 1   1
2       0 1 0   1
7       1 1 1   1

        b a x   y
0       0 0 0   1
2       0 1 0   1
3       0 1 1   1
4       1 0 0   1
6       1 1 0   1
7       1 1 1   1




        b a x   b
Gruppe 1:
2       0 1 0   1
4       1 0 0   1
Gruppe 2:
6       1 1 0   1
Gruppe 3:
7       1 1 1   1

        b a x   a
Gruppe 1:
1       0 0 1   1
2       0 1 0   1
Gruppe 3:
7       1 1 1   1

        b a x   y
Gruppe 0:
0       0 0 0   1
Gruppe 1:
2       0 1 0   1
4       1 0 0   1
Gruppe 2:
3       0 1 1   1
6       1 1 0   1
Gruppe 3:
7       1 1 1   1



        b a x   b
Gruppe 1:
2       0 1 0   1
4       1 0 0   1
Gruppe 2:
6       1 1 0   1
Gruppe 3:
7       1 1 1   1

2;6     - 1 0
4;6     1 - 0
6;7     1 1 -

b <- (a and not x) or (b and not x) or (b and a)

        b a x   a
Gruppe 1:
1       0 0 1   1
2       0 1 0   1
Gruppe 3:
7       1 1 1   1

a <- (not b and not and x) or (not b and a and not x) or (b and a and x)

        b a x   y
Gruppe 0:
0       0 0 0   1
Gruppe 1:
2       0 1 0   1
4       1 0 0   1
Gruppe 2:
3       0 1 1   1
6       1 1 0   1
Gruppe 3:
7       1 1 1   1


0;2     0 - 0
0;4     - 0 0
2;3     0 1 -
4;6     1 - 0
6;7     1 1 -
3;7     - 1 1


0;2     0 - 0
4;6     1 - 0
2;3     0 1 -
6;7     1 1 -
3;7     - 1 1
0;4     - 0 0

0;2;4;6     - - 0
2;3;6;7     - 1 -
3;7         - 1 1
0;4         - 0 0

            0   2   3   4   6   7
0;2;4;6     *   *       *   *
2;3;6;7         *   *       *   *

y <- (not x) or (a)


b <- (a and not x) or (b and not x) or (b and a)
a <- (not b and not and x) or (not b and a and not x) or (b and a and x)
y <- (not x) or (a)

        b a x   b a y
0       0 0 0   0 0 0
1       0 0 1   1 1 0
2       0 1 0   1 0 1
3       0 1 1   0 0 0
4       1 0 0   0 1 0
5       1 0 1   1 0 1
6       1 1 0   0 0 0
7       1 1 1   1 0 1


        b a x   b
0       0 0 0   0
1       0 0 1   1
2       0 1 0   1
3       0 1 1   0
4       1 0 0   0
5       1 0 1   1
6       1 1 0   0
7       1 1 1   1

        b a x   a
0       0 0 0   0
1       0 0 1   1
2       0 1 0   0
3       0 1 1   0
4       1 0 0   1
5       1 0 1   0
6       1 1 0   0
7       1 1 1   0

        b a x   y
0       0 0 0   0
1       0 0 1   0
2       0 1 0   1
3       0 1 1   0
4       1 0 0   0
5       1 0 1   1
6       1 1 0   0
7       1 1 1   1



        b a x   b
1       0 0 1   1
2       0 1 0   1
5       1 0 1   1
7       1 1 1   1

        b a x   a
1       0 0 1   1
4       1 0 0   1

        b a x   y
2       0 1 0   1
5       1 0 1   1
7       1 1 1   1



        b a x   b
Gruppe 1:
1       0 0 1   1
2       0 1 0   1
Gruppe 2:
5       1 0 1   1
Gruppe 3:
7       1 1 1   1

        b a x   a
Gruppe 1:
1       0 0 1   1
4       1 0 0   1

        b a x   y
Gruppe 1:
2       0 1 0   1
Gruppe 2:
5       1 0 1   1
Gruppe 3:
7       1 1 1   1



        b a x   b
Gruppe 1:
1       0 0 1   1
2       0 1 0   1
Gruppe 2:
5       1 0 1   1
Gruppe 3:
7       1 1 1   1

1;5     - 0 1
2       0 1 0
5;7     1 - 1

b <- (not a and x) or (not b and a and not x) or (b and x)

        b a x   a
Gruppe 1:
1       0 0 1   1
4       1 0 0   1

a <- (not b and not a and x) or (b and not a and not x)

        b a x   y
Gruppe 1:
2       0 1 0   1
Gruppe 2:
5       1 0 1   1
Gruppe 3:
7       1 1 1   1

2       0 1 0
5;7     1 - 1

y <- (not b and a and not x) or (b and x)


b <- (not a and x) or (not b and a and not x) or (b and x)
a <- (not b and not a and x) or (b and not a and not x)
y <- (not b and a and not x) or (b and x)

        b a x   b a y
0       0 0 0   0 0 1
1       0 0 1   0 1 0
2       0 1 0   0 0 0
3       0 1 1   0 1 1
4       1 0 0   1 0 0
5       1 0 1   0 1 0
6       1 1 0   1 0 1
7       1 1 1   0 0 1


        b a x   b
0       0 0 0   0
1       0 0 1   0
2       0 1 0   0
3       0 1 1   0
4       1 0 0   1
5       1 0 1   0
6       1 1 0   1
7       1 1 1   0

        b a x   a
0       0 0 0   0
1       0 0 1   1
2       0 1 0   0
3       0 1 1   1
4       1 0 0   0
5       1 0 1   1
6       1 1 0   0
7       1 1 1   0

        b a x   y
0       0 0 0   1
1       0 0 1   0
2       0 1 0   0
3       0 1 1   1
4       1 0 0   0
5       1 0 1   0
6       1 1 0   1
7       1 1 1   1



        b a x   b
4       1 0 0   1
6       1 1 0   1

        b a x   a
1       0 0 1   1
3       0 1 1   1
5       1 0 1   1

        b a x   y
0       0 0 0   1
3       0 1 1   1
6       1 1 0   1
7       1 1 1   1



        b a x   b
Gruppe 1:
4       1 0 0   1
Gruppe 2:
6       1 1 0   1

        b a x   a
Gruppe 1:
1       0 0 1   1
Gruppe 2:
3       0 1 1   1
5       1 0 1   1

        b a x   y
Gruppe 0:
0       0 0 0   1
Gruppe 2:
3       0 1 1   1
6       1 1 0   1
Gruppe 3:
7       1 1 1   1



        b a x   b
Gruppe 1:
4       1 0 0   1
Gruppe 2:
6       1 1 0   1

4;6     1 - 0

b <- (b and not x)

        b a x   a
Gruppe 1:
1       0 0 1   1
Gruppe 2:
3       0 1 1   1
5       1 0 1   1

1;3     0 - 1
1;5     - 0 1

a <- (not b and x) or (not a and x)

        b a x   y
Gruppe 0:
0       0 0 0   1
Gruppe 2:
3       0 1 1   1
6       1 1 0   1
Gruppe 3:
7       1 1 1   1

0       0 0 0
3;7     - 1 1
6;7     1 1 -


y <- (not b and not a and not x) or (a and x) or (b and a)



b <- (b and not x)
a <- (not b and x) or (not a and x)
y <- (not b and not a and not x) or (a and x) or (b and a)

        b a x   b a y
0       0 0 0   1 0 0
1       0 0 1   0 0 0
2       0 1 0   1 0 0
3       0 1 1   0 0 0
4       1 0 0   0 1 0
5       1 0 1   1 0 1
6       1 1 0   0 1 0
7       1 1 1   1 1 0


        b a x   b
0       0 0 0   1
1       0 0 1   0
2       0 1 0   1
3       0 1 1   0
4       1 0 0   0
5       1 0 1   1
6       1 1 0   0
7       1 1 1   1

        b a x   a
0       0 0 0   0
1       0 0 1   0
2       0 1 0   0
3       0 1 1   0
4       1 0 0   1
5       1 0 1   0
6       1 1 0   1
7       1 1 1   1

        b a x   y
0       0 0 0   0
1       0 0 1   0
2       0 1 0   0
3       0 1 1   0
4       1 0 0   0
5       1 0 1   1
6       1 1 0   0
7       1 1 1   0



        b a x   b
0       0 0 0   1
2       0 1 0   1
5       1 0 1   1
7       1 1 1   1

        b a x   a
4       1 0 0   1
6       1 1 0   1
7       1 1 1   1

        b a x   y
5       1 0 1   1



        b a x   b
Gruppe 0:
0       0 0 0   1
Gruppe 1:
2       0 1 0   1
Gruppe 2:
5       1 0 1   1
Gruppe 3:
7       1 1 1   1

        b a x   a
Gruppe 1:
4       1 0 0   1
Gruppe 2:
6       1 1 0   1
Gruppe 3:
7       1 1 1   1

        b a x   y
Gruppe 2:
5       1 0 1   1



        b a x   b
Gruppe 0:
0       0 0 0   1
Gruppe 1:
2       0 1 0   1
Gruppe 2:
5       1 0 1   1
Gruppe 3:
7       1 1 1   1

0;2     0 - 0
5;7     1 - 1

b <- (not b and not x) or (b and x)

        b a x   a
Gruppe 1:
4       1 0 0   1
Gruppe 2:
6       1 1 0   1
Gruppe 3:
7       1 1 1   1

4;6     1 - 0
6;7     1 1 -

a <- (b and not x) or (b and a)

        b a x   y
Gruppe 2:
5       1 0 1   1

y <- (b and not a and x)


b <- (not b and not x) or (b and x)
a <- (b and not x) or (b and a)
y <- (b and not a and x)

        b a x   b a y
0       0 0 0   0 0 1
1       0 0 1   1 1 0
2       0 1 0   0 1 1
3       0 1 1   1 1 0
4       1 0 0   0 0 1
5       1 0 1   1 1 1
6       1 1 0   1 0 0
7       1 1 1   0 0 1


        b a x   b
0       0 0 0   0
1       0 0 1   1
2       0 1 0   0
3       0 1 1   1
4       1 0 0   0
5       1 0 1   1
6       1 1 0   1
7       1 1 1   0

        b a x   a
0       0 0 0   0
1       0 0 1   1
2       0 1 0   1
3       0 1 1   1
4       1 0 0   0
5       1 0 1   1
6       1 1 0   0
7       1 1 1   0

        b a x   y
0       0 0 0   1
1       0 0 1   0
2       0 1 0   1
3       0 1 1   0
4       1 0 0   1
5       1 0 1   1
6       1 1 0   0
7       1 1 1   1



        b a x   b
1       0 0 1   1
3       0 1 1   1
5       1 0 1   1
6       1 1 0   1

        b a x   a
1       0 0 1   1
2       0 1 0   1
3       0 1 1   1
5       1 0 1   1

        b a x   y
0       0 0 0   1
2       0 1 0   1
4       1 0 0   1
5       1 0 1   1
7       1 1 1   1



        b a x   b
Gruppe 1:
1       0 0 1   1
Gruppe 2:
3       0 1 1   1
5       1 0 1   1
6       1 1 0   1

        b a x   a
Gruppe 1:
1       0 0 1   1
2       0 1 0   1
Gruppe 2:
3       0 1 1   1
5       1 0 1   1

        b a x   y
Gruppe 0:
0       0 0 0   1
Gruppe 1:
2       0 1 0   1
4       1 0 0   1
Gruppe 2:
5       1 0 1   1
Gruppe 3:
7       1 1 1   1



        b a x   b
Gruppe 1:
1       0 0 1   1
Gruppe 2:
3       0 1 1   1
5       1 0 1   1
6       1 1 0   1

1;3     0 - 1
1;5     - 0 1
6       1 1 0

b <- (not b and x) or (not a and x) or (b and a and not x)

        b a x   a
Gruppe 1:
1       0 0 1   1
2       0 1 0   1
Gruppe 2:
3       0 1 1   1
5       1 0 1   1

1;5     - 0 1
1;3     0 - 1
2;3     0 1 -

        1   2   3   5
1;5     *           *
1;3     *       *
2;3         *   *

        1   2   3   5
1;5     *           *
2;3         *   *

a <- (not a and x) or (not b and a)

        b a x   y
Gruppe 0:
0       0 0 0   1
Gruppe 1:
2       0 1 0   1
4       1 0 0   1
Gruppe 2:
5       1 0 1   1
Gruppe 3:
7       1 1 1   1

0;2     0 - 0
0;4     - 0 0
4;5     1 0 -
5;7     1 - 1

        0   2   4   5   7
0;2     *   *
0;4     *       *
4;5             *   *
5;7                 *   *


        0   2   4   5   7
0;2     *   *
0;4     *       *
5;7                 *   *

y <- (not b and not x) or (not a and not x) or (b and x)


b <- (not b and x) or (not a and x) or (b and a and not x)
a <- (not a and x) or (not b and a)
y <- (not b and not x) or (not a and not x) or (b and x)

        b a x   b a y
0       0 0 0   1 0 1
1       0 0 1   1 1 0
2       0 1 0   0 0 0
3       0 1 1   0 1 0
4       1 0 0   1 0 0
5       1 0 1   0 1 0
6       1 1 0   1 0 0
7       1 1 1   1 1 1




        b a x   b
0       0 0 0   1
1       0 0 1   1
2       0 1 0   0
3       0 1 1   0
4       1 0 0   1
5       1 0 1   0
6       1 1 0   1
7       1 1 1   1

        b a x   a
0       0 0 0   0
1       0 0 1   1
2       0 1 0   0
3       0 1 1   1
4       1 0 0   0
5       1 0 1   1
6       1 1 0   0
7       1 1 1   1

        b a x   y
0       0 0 0   1
1       0 0 1   0
2       0 1 0   0
3       0 1 1   0
4       1 0 0   0
5       1 0 1   0
6       1 1 0   0
7       1 1 1   1



        b a x   b
0       0 0 0   1
1       0 0 1   1
4       1 0 0   1
6       1 1 0   1
7       1 1 1   1

        b a x   a
1       0 0 1   1
3       0 1 1   1
5       1 0 1   1
7       1 1 1   1

        b a x   y
0       0 0 0   1
7       1 1 1   1


        b a x   b
Gruppe 0:
0       0 0 0   1
Gruppe 1:
1       0 0 1   1
4       1 0 0   1
Gruppe 2:
6       1 1 0   1
Gruppe 3:
7       1 1 1   1

        b a x   a
Gruppe 1:
1       0 0 1   1
Gruppe 2:
3       0 1 1   1
5       1 0 1   1
Gruppe 3:
7       1 1 1   1

        b a x   y
Gruppe 0:
0       0 0 0   1
Gruppe 3:
7       1 1 1   1



        b a x   b
Gruppe 0:
0       0 0 0   1
Gruppe 1:
1       0 0 1   1
4       1 0 0   1
Gruppe 2:
6       1 1 0   1
Gruppe 3:
7       1 1 1   1

0;1     0 0 -
0;4     - 0 0
4;6     1 - 0
6;7     1 1 -

0;4     - 0 0
4;6     1 - 0
0;1     0 0 -
6;7     1 1 -

        0   1   4   6   7
0;4     *       *
4;6             *   *
0;1     *   *
6;7                 *   *

        0   1   4   6   7
0;4     *       *
0;1     *   *
6;7                 *   *

b <- (not a and not x) or (not b and not a) or (b and a)

        b a x   a
Gruppe 1:
1       0 0 1   1
Gruppe 2:
3       0 1 1   1
5       1 0 1   1
Gruppe 3:
7       1 1 1   1

1;3     0 - 1
1;5     - 0 1
3;7     - 1 1
5;7     1 - 1

1;3     0 - 1
5;7     1 - 1
1;5     - 0 1
3;7     - 1 1

1;3;5;7     - - 1
1;5;3;7     - - 1

a <- x



        b a x   y
Gruppe 0:
0       0 0 0   1
Gruppe 3:
7       1 1 1   1

y <- (not b and not a and not x) or (b and a and x)


b <- (not a and not x) or (not b and not a) or (b and a)
a <- x
y <- (not b and not a and not x) or (b and a and x)

        b a x   b a y
0       0 0 0   0 1 1
1       0 0 1   1 1 1
2       0 1 0   0 0 0
3       0 1 1   0 1 1
4       1 0 0   1 0 1
5       1 0 1   0 0 1
6       1 1 0   0 1 0
7       1 1 1   0 0 1


        b a x   b
0       0 0 0   0
1       0 0 1   1
2       0 1 0   0
3       0 1 1   0
4       1 0 0   1
5       1 0 1   0
6       1 1 0   0
7       1 1 1   0

        b a x   a
0       0 0 0   1
1       0 0 1   1
2       0 1 0   0
3       0 1 1   1
4       1 0 0   0
5       1 0 1   0
6       1 1 0   1
7       1 1 1   0

        b a x   y
0       0 0 0   1
1       0 0 1   1
2       0 1 0   0
3       0 1 1   1
4       1 0 0   1
5       1 0 1   1
6       1 1 0   0
7       1 1 1   1



        b a x   b
1       0 0 1   1
4       1 0 0   1

        b a x   a
0       0 0 0   1
1       0 0 1   1
3       0 1 1   1
6       1 1 0   1

        b a x   y
0       0 0 0   1
1       0 0 1   1
3       0 1 1   1
4       1 0 0   1
5       1 0 1   1
7       1 1 1   1



        b a x   b
Gruppe 1:
1       0 0 1   1
4       1 0 0   1

        b a x   a
Gruppe 0:
0       0 0 0   1
Gruppe 1:
1       0 0 1   1
Gruppe 2:
3       0 1 1   1
6       1 1 0   1

        b a x   y
Gruppe 0:
0       0 0 0   1
Gruppe 1:
1       0 0 1   1
4       1 0 0   1
Gruppe 2:
3       0 1 1   1
5       1 0 1   1
Gruppe 3:
7       1 1 1   1


        b a x   b
Gruppe 1:
1       0 0 1   1
4       1 0 0   1

b <- (not b and not a and x) or (b and not a and not x)

        b a x   a
Gruppe 0:
0       0 0 0   1
Gruppe 1:
1       0 0 1   1
Gruppe 2:
3       0 1 1   1
6       1 1 0   1

0;1     0 0 -
1;3     0 - 1
6       1 1 0

a <- (not b and not a) or (not b and x) or (b and a and not x)

        b a x   y
Gruppe 0:
0       0 0 0   1
Gruppe 1:
1       0 0 1   1
4       1 0 0   1
Gruppe 2:
3       0 1 1   1
5       1 0 1   1
Gruppe 3:
7       1 1 1   1

0;1     0 0 -
0;4     - 0 0
1;3     0 - 1
4;5     1 0 -
3;7     - 1 1
5;7     1 - 1


0;1     0 0 -
4;5     1 0 -
0;4     - 0 0
3;7     - 1 1
1;3     0 - 1
5;7     1 - 1

Gruppe 0:
0;1     0 0 -
Gruppe 1:
4;5     1 0 -

0;1;4;5     - 0 -

0;4     - 0 0
3;7     - 1 1

0;4     - 0 0
3;7     - 1 1

1;3     0 - 1
5;7     1 - 1

1;3;5;7     - - 1

            0   1   3   4   5   7
0;1;4;5     *   *       *   *
0;4         *           *
3;7                 *           *
1;3;5;7         *   *       *   *



            0   1   3   4   5   7
0;1;4;5     *   *       *   *
1;3;5;7         *   *       *   *

y <- (not a) or (x)


b <- (not b and not a and x) or (b and not a and not x)
a <- (not b and not a) or (not b and x) or (b and a and not x)
y <- (not a) or (x)