• Vereinigung: R ◦ (S ∪ T) = (R ◦ S) ∪ (R ◦ T) beweisen
• ⟨x,y⟩∈ (S∪ T) ∘ R
  

⇔∃z: (⟨x,z⟩ ∈ S∪ T ∧ ⟨z,y⟩ ∈ R )
⇔∃z: ((⟨x,z⟩ ∈ S ∨ ⟨x,z⟩ ∈ T) ∧ ⟨z,y⟩ ∈ R )
⇔∃z: ((⟨x,z⟩ ∈ S ∧ ⟨z,y⟩ ∈ R ) ∨ (⟨x,z⟩ ∈ T ∧ ⟨z,y⟩ ∈ R ))
⇔∃z: (⟨x,z⟩ ∈ S ∧ ⟨z,y⟩ ∈ R) ∨ ∃z: (⟨x,z⟩ ∈ T ∧ ⟨z,y⟩ ∈ R )
⇔⟨x,y⟩∈  S∘ R ∨ ⟨x,y⟩ ∈ T ∘ R
⇔⟨x,y⟩∈  (S ∘ R ) ∪ (T ∘ R )