Die Menge sei ${\displaystyle {}M=\{a,b\}}$, die Potenzmenge ist dann

${\displaystyle {}{\mathfrak {P}}\,(M)=\{\emptyset ,\{a\},\{b\},\{a,b\}\}\,.}$

Die Verknüpfungstabelle für die Vereinigung ist

${\displaystyle {}\cup }$	${\displaystyle {}\emptyset }$	${\displaystyle {}\{a\}}$	${\displaystyle {}\{b\}}$	${\displaystyle {}\{a,b\}}$
${\displaystyle {}\emptyset }$	${\displaystyle {}\emptyset }$	${\displaystyle {}\{a\}}$	${\displaystyle {}\{b\}}$	${\displaystyle {}\{a,b\}}$
${\displaystyle {}\{a\}}$	${\displaystyle {}\{a\}}$	${\displaystyle {}\{a\}}$	${\displaystyle {}\{a,b\}}$	${\displaystyle {}\{a,b\}}$
${\displaystyle {}\{b\}}$	${\displaystyle {}\{b\}}$	${\displaystyle {}\{a,b\}}$	${\displaystyle {}\{b\}}$	${\displaystyle {}\{a,b\}}$
${\displaystyle {}\{a,b\}}$	${\displaystyle {}\{a,b\}}$	${\displaystyle {}\{a,b\}}$	${\displaystyle {}\{a,b\}}$	${\displaystyle {}\{a,b\}}$