Choose the most appropriate adjective to complete the sentence "He succeeded in proving his point with ________ logic."

Introduction / Context:
This sentence completion question checks your understanding of collocation and meaning. The sentence describes someone who "succeeded in proving his point" and credits this success to a certain kind of logic. Your task is to choose the adjective that best fits both the meaning and the strength of this success.

Given Data / Assumptions:
The sentence is: "He succeeded in proving his point with ________ logic." The options are:

• diabolical
• irrefutable
• rational
• analytical

We assume the writer wants to emphasise how strong and convincing the logic was.

Concept / Approach:
You should analyse:

• The outcome: he "succeeded in proving his point", so the logic was convincing.
• The connotations of each adjective and whether they match this positive outcome.
• Natural collocations: which adjective commonly appears with the noun "logic".

A natural phrase in English is "irrefutable logic" meaning logic that cannot be disproved.

Step-by-Step Solution:
Step 1: Consider "diabolical". This word usually means evil or extremely bad, and when used with "plan" or "crime" it has a negative sense. "Diabolical logic" would suggest something wicked, not simply convincing. Step 2: Check "irrefutable". It means that something cannot be disproved or argued against. "Irrefutable logic" directly explains why he succeeded in proving his point. Step 3: Examine "rational". It means based on reason or logic, but it does not specifically say how strong or unanswerable the logic is. Step 4: Look at "analytical". It means careful and systematic examination of details. While "analytical logic" is understandable, it is not a common phrase and does not emphasise the final victory in the argument. Step 5: Among all, "irrefutable" most clearly explains the success described in the sentence.

Verification / Alternative check:
Substitute each word into the sentence:

• "Diabolical logic" suggests something sinister, not suitable in a neutral or positive context.
• "Rational logic" is somewhat repetitive because logic is by nature rational.
• "Analytical logic" sounds technical but not idiomatic.
• "Irrefutable logic" is a standard expression meaning logic that no one could successfully challenge.

Therefore, "irrefutable" is the best fit.

Why Other Options Are Wrong:

• diabolical: Carries an evil or extremely negative sense, which does not match the neutral exam sentence.
• rational: Too general and does not capture the idea that no one could refute the argument.
• analytical: Focuses on method rather than persuasive power and is not a typical collocation here.

Common Pitfalls:
Students may choose "rational" because they see the link between reason and logic, but they miss the nuance of success and finality. Others may be attracted to the more difficult sounding "analytical" without thinking about natural usage. In vocabulary questions, always think about which word best captures the exact shade of meaning and which phrase you have actually seen used in real English texts.

Final Answer:
The most appropriate word is irrefutable, giving the phrase "irrefutable logic".