Wir betrachten auf der Menge

${\displaystyle {}M=\{a,b,c,d\}\,}$

die durch die Tabelle

${\displaystyle {}\star }$	${\displaystyle {}a}$	${\displaystyle {}b}$	${\displaystyle {}c}$	${\displaystyle {}d}$
${\displaystyle {}a}$	${\displaystyle {}b}$	${\displaystyle {}a}$	${\displaystyle {}c}$	${\displaystyle {}a}$
${\displaystyle {}b}$	${\displaystyle {}d}$	${\displaystyle {}a}$	${\displaystyle {}b}$	${\displaystyle {}b}$
${\displaystyle {}c}$	${\displaystyle {}a}$	${\displaystyle {}b}$	${\displaystyle {}c}$	${\displaystyle {}c}$
${\displaystyle {}d}$	${\displaystyle {}b}$	${\displaystyle {}d}$	${\displaystyle {}d}$	${\displaystyle {}d}$

gegebene Verknüpfung ${\displaystyle {}\star }$.

1. Berechne

   ${\displaystyle b\star (a\star (d\star a)).}$

2. Besitzt die Verknüpfung ${\displaystyle {}\star }$ ein neutrales Element?