Logical Reasoning

PT122 · S2 · Q7 Any fruit that is infected

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Any fruit that is infected is also rotten.

Conclusion (therefore)

Any fruit that was inspected is safe to eat.

Inspected ------------------------> Safe

Evidence

Inspected ---> ~Infected

Evaluate

The "therefore" shows us the claim we're trying to prove. On Sufficient Assumption, there are two big questions we can ask about the Conclusion:

1. Is there any New Term (that isn't ever discussed in the evidence)?

2. Can I / should I write this conclusion as a "long conditional"?

When it comes to #1, yes, there was a New Term in the conclusion that was never discussed or defined in the evidence: safe to eat.

So it's a guarantee that the correct answer will have to say "safe to eat" or something equivalent. After all, the correct answer combines with the evidence and allows us to derive the conclusion.

If you had all these claims, a = b b = c c = d you could never derive the claim a = x because we don't have any givens about "x".

When it comes to #2, we're motivated to write the conclusion as a long-conditional so that we can better see the missing piece we need.

The conclusion is one big logic path we're trying to build. Inspected ----------------------------------> Safe

The evidence and the answer we pick are the building blocks for that logic path. The one premise we have is this: No fruit that was inspected is infected.

The other statement, "if infected, then rotten" is irrelevant to our conclusion. Our conclusion is about inspected fruit, and none of the inspected fruit is infected. So that first sentence is what you might call a "Fake Premise". It looks like it could be relevant, but it has nothing to do with our conclusion.

So how do we turn our one premise (the 2nd sentence) into a conditional?

No A's are B = All A's are ~B = A → ~B No inspected are infected = All inspected are not infected Inspected → ~Infected

We're trying to prove this,

Inspected ----------------------------------> Safe

and this is what we have so far

Inspected ----> ~Infected

So what are we missing? ~Infected ---------------> Safe

If you want to do this problem more conversationally, then just work backwards from the conclusion. You're trying to prove that "anything inspected is safe".

What were we told about stuff that was inspected? We were told that it isn't infected.

What were we told about stuff that isn't infected? Nothing.

So we know that a possible answer could be "if isn't infected, then safe to eat"

Goal

We're looking for

"if isn't infected, then safe to eat"

but since we know that Sufficient Assumption loves to hide the correct answer via contrapositive, we should also look for

7.

The conclusion of the argument follows logically if which one of the following is assumed?

  1. It is not safe to

    Unrelated to Goal

    As soon as we see this answer contains "rotten", we know it's .... rotten. :) That first sentence was not actually a premise. It doesn't relate to inspected fruit, so it won't have anything to do with proving that "inspected fruit is safe". Sentences of the form "It is A to be B" get diagrammed like this: B ? A How do we know? Ask yourself how you would diagram the sentence, "It is wrong to lie to your mom". if you did something wrong ? lied to mom or if you lied to mom ? did something wrong The 2nd one is the correct translation. If you combine the two sentences we're given in the evidence with this answer, can you derive the conclusion? 1st: Infected ? Rotten (A): Rotten ? ~Safe 2nd: Infected ? ~Inspected We can't derive this logic path Inspected ? Safe The easiest way to see that is that we only have "not safe" on the right side of the arrow. We need to have "safe" on the right side of the arrow.

    9% picked this

  2. It is safe to eat

    Unrelated to Goal

    As soon as we see this answer contains "rotten", we know it's .... rotten. :) That first sentence was not actually a premise. It doesn't relate to inspected fruit, so it won't have anything to do with proving that "inspected fruit is safe". Sentences of the form "It is A to be B" get diagrammed like this: B ? A If you combine the two sentences we're given in the evidence with this answer, can you derive the conclusion? 1st: ~Rotten ? ~Infected (B): ~Rotten ? Safe 2nd: Inspected ? ~Infected We can't derive this logic path Inspected ? Safe We can get from Inspected to ~Infected, but we don't have a way to get from ~Infected to Safe. That's because this answer is attaching itself to ideas in the first sentence, and the first sentence isn't connected in any way to "Inspected fruit".

    18% picked this

  3. It would have been safe

    Wrong Tense Too Narrow

    The conclusion is in simple present tense. This answer is in some weird counterfactual conditional tense. That's already showing us it doesn't match. This conditional allows us to say "Any infected fruit that would have been inspected would have been safe to eat". This is a narrower claim than what we're trying to prove: "Any fruit that was inspected is safe". This answer only establishes that infected fruit was safe to eat. It doesn't establish that uninfected fruit was safe to eat.

    2% picked this

  4. It is not safe to

    Opposite Logic

    We're looking for ~Infected ? Safe to eat This gives us the illegal opposite version of that: Infected ? ~Safe to eat

    17% picked this

  5. Correct

    It is safe to eat

    Why this is right

    This gives us exactly what we were looking for (and given how annoying it is to explain the wrong answers, keep in mind how important it is on Sufficient Assumption to come to the answers already knowing what the correct answer should say. It's a question type where you don't need to work Wrong to Right. Solve for the missing idea upfront and then just go find it in the answers). When we combine the 2nd sentence Inspected ? ~Infected with answer choice (E) ~Infected ? Safe to eat we can derive the logic path of the conclusion Inspected -------------------> Safe to eat

    Skill tested: Sufficient Assumption · how this choice captures the argument's function is the move to repeat next time.

    54% picked this

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