Define sets S, T and E as below:

S = {n ∈ Z | n ≡ 0 (mod 4)}

T = {n ∈ Z | n ≡ 2 (mod 4)}

E = {n ∈ Z | n ≡ 0 (mod 2)}.

Prove that S × T ⊂ E × E.