or any integer n$,$ define Sn $=\{$nx $|$ x in Z$\}$ as before. For any integers a$,$ b$,$ and n$,$

if ab $/$ in Sn$,$ then neither a nor b is a member of Sn$.$

Hint: Don$$t try to prove the two conclusions using the same proof by contradiction

subproof. You$$ll want two separate $($but very similar$)$ subproofs for this.