Image Preserves Union Image Preserves Union For f:X→Y and Ai⊆X for all i∈If(⋃i∈IAi)=⋃i∈If(Ai) Proofx∈f(∪i∈IAi)⟺∃y∈∪i∈IAi,(f(y)=x)⟺∃i∈I,∃y∈Ai,(f(y)=x)⟺∃i∈I,x∈f(Ai)⟺x∈∪i∈If(Ai)