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Solutions
Correct Answer is: to have believe
Option (a) contains an error.
Detailed explanation of error: After to have, we require the past participle (V3) to form the perfect infinitive.
So, to have believe ✗ should be to have believed ✓.
The perfect infinitive is appropriate because the believing happened before the time of realisation ( I was).
Corrected sentence: How foolish I was to have believed that young woman! (You could also use the simple infinitive to believe for a general comment, but the exam tests V3 after “to have”.)
Grammatical rule used: Perfect infinitive = to have + V3, showing an action earlier than the time expressed by the main verb.
Example: She was lucky to have escaped the fire.
Information booster: We often use the perfect infinitive after evaluative adjectives ( foolish, wise, fortunate, careless) to show the earlier action: It was careless to have left the door open.