Proposition 1.1.10.  Let U be a set, S, T ⊆ U. Then:
S ∩ T = T ∩ S
Proof.
  • Let x ∈ S ∩ T. Then x ∈ T ∩ S:
    We show that x ∈ T and x ∈ S:
    x ∈ S ∩ T ⇒def x ∈ S and x ∈ T
  • Let x ∈ T ∩ S. Then x ∈ S ∩ T:
    We show that x ∈ S and x ∈ T:
    x ∈ T ∩ S ⇒def x ∈ T and x ∈ S
References.