Lösungen / Solutions

1

Solve[2 - Tan[x] == 1, {x}]

30 Degree

Cos[30 Degree]

Solve[4 - Cos[30 Degree] - x + x^2 == 4, {x}]

N[%]

2

Remove[x, a, b, Wtab]

Programm:

\(\(Wtab[f_, m_] := 
        Module[{tabb, tabZ, res, newtabX, u, exttabX, output, 
            output1}, \ 
Attributes[
              f] = {Listable}; 
tabb[
              1] = {{0}, {1}}; 
tabb[u_] := 
            Flatten[Table[
                Append[\(tabb[u - 1]\)[\([k]\)], w], {k, 1, 
                  Length[tabb[u - 1]]}, {w, 0, 1}], 1]; 
          tabZ[u_] := \ tabb[u] /. {0 -> False, 1 -> True}; 
          res = Table[
              Apply[f, \(tabZ[m]\)[\([n]\)]], {n, 1, Length[tabZ[m]]}]; 
          newtabX = Transpose[tabZ[m]]; 
u = 
            Length[newtabX]; 
\ \ \ \ \ exttabX = 
            Transpose[
              Append[newtabX, res]]; 
\ \ \ \ \ Prepend[exttabX, 
                Append[Range[u], {expr}]] /. {True -> 1, False -> 0} // 
            MatrixForm];\)\)
sub[x_, y_] := Or[Not[x], y]; 
    Attributes[sub] = {Listable};
bij[x_, y_] := And[sub[x, y], sub[y, x]]; 
    Attributes[bij] = {Listable};
orExc[x_, y_] := Not[bij[x, y]]; 
    Attributes[bij] = {Listable};
asUsual[f_] := 
      StringReplace[
        ToString[
          TraditionalForm[f]], {"!" -> "¬"}]

a

f[x_, y_] := And[Not[x], y]

Wtab[f, 2]

b

f[x_, y_] := Or[And[Not[x], y], x]

Wtab[f, 2]

c

f[x_, y_] := sub[Or[And[Not[x], y], x], y]

Wtab[f, 2]

3

a = Table[n, {n, 3, 45, 3}]

b = Table[n, {n, 4, 44, 4}]

c = Table[n, {n, 5, 45, 5}]

a

Intersection[a, b]

b

Union[a, b]

c

Complement[c, Union[a, b]]

Union[a, b]

d

Union[Intersection[a, b], Complement[c, Union[a, b]]]

4

<< Graphics`Arrow`

Show[
        Graphics[{PointSize[0.03], Point[{0. , 0. }], Arrow[{1, 1}, {2, 1}], 
            Arrow[{2, 1}, {3, 1}], Arrow[{3, 1}, {2, 1}], 
            Arrow[{2, 1}, {1, 1}], Arrow[{1, 1.05}, {3, 1.05}], 
            Arrow[{3, 1.05}, {1, 1.05}], Arrow[{4, 1}, {5, 1}], 
            Arrow[{5, 1}, {4, 1}], Arrow[{3, 1.05}, {1, 1.05}], 
            Point[{4, 1}], Point[{0, 0}], Line[{{0, 0}, {0, 1.1}}], 
            Line[{{0, 0}, {5, 0}}]}]];

5

<< Graphics`InequalityGraphics`

InequalityPlot[(-y ≥ -2 
                x)   &&  (y ≤ -x + 3)  &&  (x >= 
              0),  {x,  0,  4},  {y, -2,  3} ];