Let P be the set of all prime numbers. A subset S ⊆ Z is called special if and only if ∀x ∈ S, ∃y ∈ S, |x − y| ∈ P.  

(a) Prove that the set {2, 5, 7, 17} is not special.  

(b) Prove or disprove: If S and T are special, then S ∪ T is special.  

(c) Prove or disprove: If S and T are special, then |S × T| > 4.

d) Let m, n ∈ Z. Define sets S = { x ∈ Z : x | m } and T = { y ∈ Z : n | y }. Prove that S ⊆ T if and only if |n| = 1.