Logical reasoning PrepTest 122 · Section 2 · Question 7

Incorrect. Rotten → not Safe to eat. This answer chains together with the first statement, but it has a term that can't line up with the conclusion. The necessary condition of the conclusion is Safe to eat, and the necessary condition of this answer is not Safe to eat, so even when we take the contrapositive they won't line up, and thus this answer doesn't connect anything to the conclusion.

Incorrect. not Rotten → Safe to eat. While this answer does line up with the conclusion's necessary condition, it doesn't connect to anything from the premises since the necessary condition it would "chain together" with is Rotten, not not Rotten.

Incorrect. Throw this answer out as soon as it starts using weird language ("would have been") that doesn't line up with the stimulus.

Incorrect. Infected → not Safe to eat. Be careful with these diagrams! The conditional keyword here is "any," introducing a sufficient condition. With the statement diagrammed correctly, we can see that this answer is the negated version of our anticipation, so it's incorrect.

Correct. Argument or Facts:
Argument

Valid or Flawed:
Flawed

Question Type:
Strengthen with Sufficient Premise

Stimulus Summary:
Infected → Rotten
Inspected → not Infected
Therefore - Inspected → Safe to eat

Answer Anticipation:
This is an interesting Strengthen with Sufficient Premise question, and we'll see why in a second!

Conditional logic-based Strengthen with Sufficient Premise questions tend to either chain conditionals together, or apply a conditional to a specific case. When the conclusion is conditional, we're usually in the former camp.

Here, however, the premises don't chain together. The shared term is "Infected," but it shows up in the sufficient condition of the first premise and negated in the necessary condition of the second. If we take the contrapositive of the second statement, then the premises would share a sufficient condition, which doesn't allow us to chain them together (we could make a some inference using quantifier rules, but the conclusion is a conditional, so that's not helpful).

Since we can't chain them together, we should see how they overlap with the conclusion. Looking there, we can see that the second premise shares a sufficient condition with the conclusion, but the first premise doesn't share any terms with it. The first premise, then, is irrelevant to the argument since it doesn't connect to either the other premise or the conclusion.

With that noted, we can anticipate our answer. The argument establishes that inspected food isn't infected; the argument concludes that inspected food is safe to eat. For that argument to work, it must be the case that food that isn't infected is safe to eat (not Infected → Safe to eat; not Safe to eat → Infected). Let's find that answer.

Answer Explanation:
not Infected → Safe to eat. This answer bridges the gap in our argument, connecting the second premise to the conclusion and thus allowing the conclusion to follow logically.

Key Takeaway:
Most Strengthen with Sufficient Premise questions that chain together conditional statements will utilize all premises in the chain, but not all of them do. When a statement neither chains together with another premise nor connects to the conclusion, it's likely there to distract you!