Theorem
The empty set Ø is a subset of every set including itself and the universal set S
i.e. Ø ⊆ A ∀A ⊆ S.
Proof
By definition of the subset, Ø ⊆ A is true because all of the elements in Ø (of which there are none) are in A. Thus Ø ⊆ A is vacuously true.
$ \blacksquare $
