Concept:
Representative elements are the \(s\)-block and \(p\)-block elements of the periodic table (Groups 1, 2 and 13--18). Transition (\(d\)-block) and inner transition (\(f\)-block) elements are not representative elements.
Step 1: Examine each set.
• Set I: \(3\) (Li), \(33\) (As), \(53\) (I), \(87\) (Fr)
All are \(s\)- or \(p\)-block elements. \checkmark
• Set II: \(2\) (He), \(10\) (Ne), \(22\) (Ti), \(36\) (Kr)
Titanium (\(22\)) is a \(d\)-block element. \(\times\)
• Set III: \(9\) (F), \(35\) (Br), \(51\) (Sb), \(88\) (Ra)
All are representative (\(p\)-block and \(s\)-block) elements. \checkmark
• Set IV: \(17\) (Cl), \(25\) (Mn), \(37\) (Rb), \(48\) (Cd)
Manganese (\(25\)) and Cadmium (\(48\)) are \(d\)-block elements. \(\times\)
Step 2: Identify the correct sets.
Only Sets I and III contain representative elements exclusively.
Step 3: Final conclusion.
\[
\boxed{\text{I \& III only}}
\]
Hence, the correct option is \(\boxed{(C)}\).