Step 1: Identify the vessel. The posterior inferior cerebellar artery (PICA) is the largest branch of the vertebral artery and supplies the lateral part of the medulla and the inferior cerebellum.
Step 2: Localise the deficit. Occlusion of PICA (or the vertebral artery) infarcts the dorsolateral medulla, producing lateral medullary syndrome, also called Wallenberg syndrome. So option a is correct.
Step 3: Clinical clues of Wallenberg syndrome include ipsilateral facial pain/temperature loss, contralateral body pain/temperature loss (crossed sensory loss), ipsilateral Horner's syndrome, vertigo, dysphagia and ipsilateral cerebellar ataxia.
Step 4: Why the others are wrong: Weber syndrome is a midbrain lesion (PCA/basilar perforators), and medial medullary syndrome is due to anterior spinal artery or vertebral artery branches supplying the medial medulla, not PICA.