Actually, the set is not empty, but has three elements, each involving preventing access to firearms by a circumscribe group of people: convicted violent felons, the psychotic, and unsupervised children.
2) Psychotic? Sez who? Have you ever filled out a Form 4473? Gun control advocates' concerns about mental health are illegitimate, as their advocacy is aimed at harassing the honest, sane gun-owner.
3) Unsupervised children? Have you ever filled out a Form 4473? Gun control advocates' concern is again illegitimate, as their activities are again aimed at harassing the honest, sane gun owner.
No, sir.
"[T]he legitimate concerns of gun-control advocates" is the empty set.