A:{1,2,3,4};

B:{3,4,5};

C:{4,5,6,7};

S:union(A,B,C);

Kommutativgesetze

union(union(A,B),C)=union(A,union(B,C));

intersection(intersection(A,B),C)=intersection(A,intersection(B,C));

Assoziativgesetze

union(union(A,B),C)=union(A,union(B,C));

intersection(intersection(A,B),C)=intersection(A,intersection(B,C));

Distributivgesetze

union(A,intersection(B,C))=intersection(union(A,B),union(A,C));

intersection(A,union(B,C))=union(intersection(A,B),intersection(A,C));

Gesetze für die neutralen Elemente

union(A,{})=A;

intersection(A,S)=A;

Gesetze für die dominanten Elemente

union(A,S)=S;

intersection(A,{})={};

Gesetze für das komplementäre Element

union(A,setdifference(S,A))=S;

intersection(A,setdifference(S,A))={};

Idempotenzgesetze

union(A,A)=A;

intersection(A,A)=A;

Gesetz für das doppelte Komplement

KA:setdifference(S,A);

KKA:setdifference(S,KA)=A;

Absorptionsgesetze

union(A,intersection(A,B))=A;

intersection(A,union(A,B))=A;

Gesetze von de Morgan

KAorB:setdifference(S,union(A,B));

KA:setdifference(S,A);

KB:setdifference(S,B);

KAorB=intersection(KA,KB);

KAandB:setdifference(S,intersection(A,B));

KAandB=union(KA,KB);