Zur Navigation springen Zur Suche springen

Wir betrachten die Mengen

${\displaystyle L=\{1,2,3,4,5,6,7,8\},\,M=\{a,b,c,d,e,f,g,h,i\}{\text{ und }}N=\{R,S,T,U,V,W,X,Y,Z\}}$

und die Abbildungen ${\displaystyle {}\varphi \colon L\rightarrow M}$ und ${\displaystyle {}\psi \colon M\rightarrow N}$, die durch die Wertetabellen

 ${\displaystyle {}x}$ ${\displaystyle {}1}$ ${\displaystyle {}2}$ ${\displaystyle {}3}$ ${\displaystyle {}4}$ ${\displaystyle {}5}$ ${\displaystyle {}6}$ ${\displaystyle {}7}$ ${\displaystyle {}8}$ ${\displaystyle {}\varphi (x)}$ ${\displaystyle {}c}$ ${\displaystyle {}i}$ ${\displaystyle {}a}$ ${\displaystyle {}g}$ ${\displaystyle {}d}$ ${\displaystyle {}e}$ ${\displaystyle {}h}$ ${\displaystyle {}b}$

und

 ${\displaystyle {}y}$ ${\displaystyle {}a}$ ${\displaystyle {}b}$ ${\displaystyle {}c}$ ${\displaystyle {}d}$ ${\displaystyle {}e}$ ${\displaystyle {}f}$ ${\displaystyle {}g}$ ${\displaystyle {}h}$ ${\displaystyle {}i}$ ${\displaystyle {}\psi (y)}$ ${\displaystyle {}X}$ ${\displaystyle {}Z}$ ${\displaystyle {}Y}$ ${\displaystyle {}S}$ ${\displaystyle {}Z}$ ${\displaystyle {}S}$ ${\displaystyle {}T}$ ${\displaystyle {}W}$ ${\displaystyle {}U}$

gegeben sind.

1. Erstelle eine Wertetabelle für ${\displaystyle {}\psi \circ \varphi }$.
2. Sind die Abbildungen ${\displaystyle {}\varphi }$, ${\displaystyle {}\psi }$, ${\displaystyle {}\psi \circ \varphi }$ injektiv?
3. Sind die Abbildungen ${\displaystyle {}\varphi }$, ${\displaystyle {}\psi }$, ${\displaystyle {}\psi \circ \varphi }$ surjektiv?