Step 1: Check the Assertion.
Peptic ulcers caused by H. Pylori infection keep coming back if the bacteria is only suppressed with acid lowering drugs and not properly cleared. Trials have shown that a full eradication regimen against H. Pylori heals the ulcer and, unlike plain acid suppression, also stops most relapses. So the Assertion is true.
Step 2: Check the Reason.
The Reason claims that H. Pylori is the only cause of peptic ulcer. This is not correct. Long term use of NSAIDs is a major and well known cause of peptic ulcers, and rare conditions such as Zollinger Ellison syndrome, where a tumour secretes excess gastrin, also produce ulcers without any H. Pylori infection. So the Reason is false.
Step 3: Decide the relationship.
Since the Assertion is true but the Reason is false, the Reason cannot be an explanation for the Assertion.
Step 4: Rule out the other codes.
The two options that call R true do not fit, since R is factually wrong. The option that calls A false does not fit either, since eradication therapy genuinely is the regimen that both heals the ulcer and prevents relapse.
Final Answer:
The Assertion is true but the Reason is false.