Lösungen/Solutions/E1S1AlUe/Ex3

L=Lektion/Leçon-- Sprechstunde/heures de consultation
W=Work/Arbeit/Travail
Programme vgl. Ue2
Programmes voir ex2

Ueb/Ex 1      W

kNF = ¬ x1 && ¬ x2 && ¬ x3  || ¬ x1 && x2 && x3  || 
        x1 && ¬ x2 && ¬ x3 ; asUsual[aNF]

aNF  =  ¬ ((x1 || 
                  x2 || ¬ x3)  && (x1 || ¬ x2 || 
                  x3)  && (¬ x1 || 
                  x2 || ¬ x3)  && (¬ x1 || ¬ x2 || 
                  x3)  && (x1 || x2 || 
                  x3) );
asUsual[aNF]

aNF  //. {Not[And[x__, y_]] :> Or[Not[x], Not[y]]}
 // 
      asUsual

aNF  //. {Not[And[x__, y_]] :> 
            Or[Not[x], Not[y]], 
Not[
              Or[x__, y_]] :> 
            And[Not[x], Not[y]]}
 // asUsual

Ueb/Ex 2      L

Ueb/Ex 3      L

Ueb/Ex 4      W

a

f[x_] := Sin[x];  g[x_] := Cos[x]

f[g[x]]

g[f[x]]

b

f[x_] := E^x;  g[x_] := Log[x]

f[g[x]]

g[f[x]]

c

f[x_] := x^(3/5);  g[x_] := 2  Cos[x] - x^2 + Sqrt[x]

f[g[x]]

g[f[x]]

d

f[x_] := x^2 + x;  g[x_] := Sqrt[x] - x^3; z[x_] := 1/x;

f[g[x]]

g[f[x]]

f[f[z[x]]]

z[g[f[x]]]

e

f[x_] := Log[x^2/(1 - x)];
 g[x_] := x^2/(1 + x); z[x_] := x/(x^2 - 1);

f[g[x]]

g[f[x]]

f[f[z[x]]]

z[g[f[x]]]