In this grammar improvement question, choose the best alternative to replace the underlined part: I purposely did that with a view to offend her.

Introduction / Context:
This question examines your knowledge of fixed phrases in English, specifically with a view to, which is commonly used to express intention or purpose. While the words view and offend might tempt you to add different prepositions or verb forms, there is a standard pattern that must be followed.

Given Data / Assumptions:
- Original sentence: I purposely did that with a view to offend her. - Underlined part: with a view to offend her. - Options suggest variations with different prepositions and verb forms. - The intended meaning is that the speaker acted deliberately in order to offend her.

Concept / Approach:
The standard expression is with a view to plus gerund, meaning with the intention of doing something. Therefore, the verb that follows to should be in its ing form, not base form. Among the options, with a view to offending her fits this pattern perfectly. Any change to of or that, or keeping the verb in base form, breaks the idiomatic structure.

Step-by-Step Solution:
Step 1: Recognise that with a view to is a fixed prepositional phrase expressing purpose. Step 2: Recall that preposition to in such phrases is followed by a gerund, not a base verb. Step 3: Change offend to offending, giving with a view to offending her. Step 4: Option C matches this corrected form exactly. Step 5: Option A, with a view of offending her, changes the preposition and is less idiomatic. Step 6: Option B, with a view that I offend her, is ungrammatical and awkwardly structured. Step 7: No improvement is wrong because the original verb form is incorrect after to in this phrase.

Verification / Alternative check:
Check with similar sentences: He went abroad with a view to improving his career prospects. The organisation held a meeting with a view to resolving the dispute. In both examples, improving and resolving are gerunds following with a view to. Rewriting the original as I purposely did that with a view to offending her brings it in line with this standard pattern.

Why Other Options Are Wrong:
With a view of offending her in option A is not the standard collocation, as the expression traditionally uses to, not of. With a view that I offend her in option B is clumsy, introduces an unnecessary clause, and does not follow normal English usage. No improvement in option D cannot be correct because to offend must be changed to to offending after with a view to.

Common Pitfalls:
Learners often confuse the infinitive marker to with the preposition to. In with a view to, to is a preposition and must be followed by a gerund, whereas in patterns like to offend, it is part of an infinitive. Confusing these roles leads to errors in verb form. Remember that fixed phrases such as with a view to, look forward to, and be committed to are always followed by ing verbs.

Final Answer:
The correct improvement is with a view to offending her, so the answer is option C.