Benutzer:Alfi

Wiki-Quelltext dieser Seite.

= Uebung 1 =

==Aufgabe Folie 12==

Flaci: https://flaci.com/Tiqnewz89


==Aufgabe Folie 16==
{| border="1px" cellpadding="8" cellspacing="0"
|-style="text-align: center;background-color:lightgrey;"
|| '''$A$''' || '''$B$''' || '''$\lnot A$''' || '''$\lnot B$''' || '''$A \rightarrow B$''' || '''$\lnot B \land (A \rightarrow B)$''' || $\lnot B \land (A \rightarrow B) \Rightarrow \lnot A$
|-style="text-align: center;"
|| w || w || f || f || w || f || w
|-style="text-align: center;"
|| w || f || f || w || f || f || w
|-style="text-align: center;"
|| f || w || w || f || w || f || w
|-style="text-align: center;"
|| f || f || w || w || w || w || w
|-
|}


==Aufgabe Folie 21 - 1==

 Satz:  Wenn n gerade ist, dann ist auch n² ungerade.
 Beweis: Ein ungerades n lässt sich als auch als 2k+1 bezeichnen.
 n² entspräche dann (2k+1)²
 (2k+1)² = 4k² + 4k + 1 
         = 2 * (2k² + 2k) + 1
         = 2 * (    a   ) + 1
 (2k+1)² = 2a + 1, q.e.d.


==Aufgabe Folie 21 - 2==

 Satz:  Die Summe dreier aufeinanderfolgender natürlicher Zahlen ist stets durch 3 teilbar.
 Beweis: Drei aufeinanderfolgende Zahlen kann man auch schreiben als n, n + 1 und n +2
 n + n + 1 + n + 2 = 3n + 3
                   = 3 * (n+1), q.e.d.


==Aufgabe Folie 22==
{| border="1px" cellpadding="8" cellspacing="0"
|-style="text-align: center;background-color:lightgrey;"
|| '''$A$''' || '''$B$''' || '''$\lnot A$''' || '''$\lnot B$''' || '''$A \rightarrow B$''' || '''$\lnot A \lor B$''' || '''$B \lor \lnot A$''' || '''$\lnot \lnot B \lor \lnot A$''' || '''$\lnot B \rightarrow \lnot A$'''
|-style="text-align: center;"
|| w || w || f || f || style="background: yellow;"|w || w || w || w || style="background: yellow;"|w
|-style="text-align: center;"
|| w || f || f || w || style="background: yellow;"|f || f || f || f || style="background: yellow;"|f
|-style="text-align: center;"
|| f || w || w || f || style="background: yellow;"|w || w || w || w || style="background: yellow;"|w
|-style="text-align: center;"
|| f || f || w || w || style="background: yellow;"|w || w || w || w || style="background: yellow;"|w
|-
|}


{| border="1px" cellpadding="8" cellspacing="0"
|-style="text-align: center;background-color:lightgrey;"
|| '''$A$''' || '''$B$''' || '''$\lnot A$''' || '''$\lnot B$''' || '''$A \rightarrow B$''' || '''$A \land \lnot B$'''
|-style="text-align: center;"
|| w || w || f || f || w || f
|-style="text-align: center;"
|| w || f || f || w || f || w
|-style="text-align: center;"
|| f || w || w || f || w || f
|-style="text-align: center;"
|| f || f || w || w || w || f
|-
|}

==Aufgabe Folie 27==
{| border="1px" cellpadding="8" cellspacing="0"
|-style="text-align: center;background-color:lightgrey;"
|| '''$A$''' || '''$B$''' || '''$C$''' || '''$\lnot A$''' || '''$\lnot B$''' || '''$\lnot C$''' || '''$A \rightarrow B$''' || '''$B \rightarrow C$'''
|-style="text-align: center;background-color:orange;"
|| w || w || w || f || f || f || w || w 
|-style="text-align: center;"
|| w || f || w || f || w || f || f || w
|-style="text-align: center;"
|| w || w || f || f || f || w || w || f
|-style="text-align: center;"
|| w || f || f || f || w || w || f || w
|-style="text-align: center;background-color:orange;"
|| f || w || w || w || f || f || w || w
|-style="text-align: center;"
|| f || w || f || w || f || w || w || f
|-style="text-align: center;background-color:orange;"
|| f || f || w || w || w || f || w || w 
|-style="text-align: center;background-color:limegreen;"
|| f || f || f || w || w || w || w || w
|-
|}
Antwort auf 27-2: Man kann aus den Gegebenheiten nichts schließen.

==Aufgabe Folie 34==
Eigenschaften von Äquivalenzrelationen:
*Transitiv ( $\forall x,y,z\in M:xRy\land yRz\Rightarrow xRz$ )
*Refelexiv ( $\forall x\in M:xRx $)
*Symmetrisch ( $ \forall x,y\in M:(xRy\Rightarrow yRx) $ )