Published by Think Clearly Prep · Updated .
Translate the direction before using the rule
“If a proposal is approved, it received a review” means approved → reviewed. An approved proposal without a review violates the rule. A reviewed proposal without approval does not: review can be required without being enough.
Words such as only, unless, and requires can tempt you to follow sentence order. Instead ask what is being ruled out. “Only reviewed proposals are approved” rules out approval without review, so it has the same direction: approved → reviewed.
The four patterns
A helpful counterexample is a building with two entrances. If someone uses the north entrance, they enter the building. Entering the building does not prove they used the north entrance; they may have used the south entrance. Not using the north entrance does not prove they stayed outside.
- Valid: A → B; A is true; therefore B is true.
- Valid contrapositive: A → B; B is false; therefore A is false.
- Invalid reversal: A → B; B is true; therefore A is true.
- Invalid negation of the trigger: A → B; A is false; therefore B is false.
Work through “unless”
“The shipment will not leave unless the invoice is paid” rules out leaving while unpaid. Write leaves → paid, or its equivalent contrapositive not paid → does not leave. Payment alone does not guarantee departure: a weather delay could still stop the shipment.
Do not turn a condition about permission into a prediction that the permitted event must occur. Translate the restriction, then keep other possible causes separate.
Necessary assumptions are a related but different task
A necessary-assumption question asks which unstated claim the argument needs. It does not always ask you to translate an explicit if–then sentence. Consider: “The museum’s only entrance closes at six, so no new visitor can enter after six.” The reasoning needs the assumption that visitors cannot enter by some other route after the entrance closes.
Negating that assumption allows entry by another route and breaks the inference. By contrast, the claim that every visitor enjoys museums is irrelevant to the entry conclusion. The negation test checks whether denying a candidate undermines the inference; it does not require proving the conclusion false in every possible world.
Practice without adding a premise
Rule: Every certified instrument passed inspection. Fact: Instrument M passed inspection. Can you conclude that M is certified?
No. The rule is certified → inspected. M may have passed inspection while waiting for certification or may never have been submitted for certification. Those possibilities show why the conclusion is not forced; they are counterexamples, not new facts you must assume actually occurred.
Now change the fact: M did not pass inspection. You can conclude that M is not certified under the given rule. This is the contrapositive.
A short review routine
- Name the trigger and the required result.
- Write the contrapositive by reversing the direction and negating both conditions.
- Construct one case where the required result occurs without the trigger.
- Check whether the question asks what must follow, what is required, or what would be enough.