Fill in the blank with the correct preposition in the sentence I am ____ this crime.

Introduction / Context:
Preposition based fill in the blank questions test whether you know the fixed combinations of adjectives and prepositions that native speakers use. The sentence here is I am ____ this crime. We must choose the adjective and preposition combination that correctly expresses that the speaker did not commit the crime and is free from guilt.

Given Data / Assumptions:

The base structure is I am plus an adjective phrase and the object this crime.
The intended meaning in typical exam context is that the speaker wants to deny guilt or responsibility.
We must choose one option that is both grammatically correct and semantically appropriate.

Concept / Approach:
English uses specific collocations, such as innocent of a crime, guilty of a crime, ignorant of a fact, and indebted to a person. Knowing these patterns is essential. The adjective innocent is the standard word used to say that someone did not commit a crime. It is typically followed by the preposition of when we mention the crime or charge. Thus the strongest candidate is innocent of this crime. Other options either use the wrong preposition or the wrong adjective for this context.

Step-by-Step Solution:
Step 1: Consider the meaning we want: the speaker wants to say that he or she did not commit the crime. Step 2: Recall the common phrase used in legal and everyday English: an accused person can be innocent of a crime. Step 3: Check the collocation innocent of a crime and see that it fits directly with this crime. Step 4: Test the full sentence I am innocent of this crime and confirm that it sounds natural and precise. Step 5: Eliminate alternatives that either sound unnatural or change the intended meaning.

Verification / Alternative check:
We can verify the choice by imagining related sentences such as He was declared innocent of all charges or She is innocent of any wrongdoing. In each case the preposition of directly follows innocent, and the object is a crime or accusation. Substituting our phrase into this pattern confirms that I am innocent of this crime is the expected and idiomatic expression in English.

Why Other Options Are Wrong:
Option A ignorant on this crime is incorrect because the usual collocation is ignorant of something, and more importantly ignorance does not directly express lack of guilt.
Option C indebted to this crime is wrong because indebted is used with to and usually refers to a person or institution to whom one owes thanks or money, not to a crime.
Option D ignoring this crime changes the meaning completely and suggests that the speaker is aware of the crime but chooses not to pay attention, which is not the same as denying guilt.
Option E unaware from this crime combines the wrong preposition from with unaware and still fails to express the idea of legal innocence.

Common Pitfalls:
Many learners pick answers that look similar to familiar phrases but miss the correct preposition, for example ignorant on instead of ignorant of or unaware from instead of unaware of. Exams often include such near misses to test your knowledge of collocations. A good strategy is to learn common adjective plus preposition pairs, especially for legal and emotional vocabulary such as guilty of, proud of, afraid of, satisfied with, and bored with.

Final Answer:
The correct and idiomatic phrase is innocent of this crime, so the complete sentence is I am innocent of this crime.