Correct option is (a) True
Easiest explanation: Case1 (Oxygen-free acids)
Anodic reaction: M==M>^+n+ne
Cathodic reaction: 2H^++2e==>H2
Case2 (Oxygenated acids)
Anodic reaction: M==>M^+n+ne
Cathodic reaction: 2H^++2e==>H2, O2+4H^++4e==>2H2O
This oxygen reduction increases the cathodic rate which correspondingly increases the anodic rate or corrosion rate.