#7 - Any fruit that is infected is also rotten. No fruit

[Sherry001]

Awesome! Thank you . But just a quick question. ( clearly I need to visit my bibles again )!

I totally get this .
A->B
A->C
... A->B->C



But would this be correct as well ?

A->B
A->C
...A->C->B

[Jon Denning]

It depends on what you mean by "correct." That is, how you classify those various statements as either "known premise," "conclusion," and "given answer choice" will dictate what you can do with them!

In the first, if A B is a premise, and A C is the conclusion we're trying to prove, then we need an answer that forms the chain A B C, meaning we need the B C statement.

In the second, if A B is a premise and A C the conclusion, then adding C B wouldn't tell us anything.

BUT, if we had A C as premise and A B as conclusion then the chain you show with A C B (made by adding C B) would prove the A B conclusion.

So it all depends on how you're using/given each piece and what you're trying to do.

[ShannonOh22]

Hi Powerscore,

I fully see how E is correct on this question, but I'm struggling to figure out why D is incorrect.

Here is my pattern of reasoning:

inspected -> infected -> safe to eat

According to the contrapositive, wouldn't this also equal

safe to eat-> infected -> inspected

This is what answer choice D is saying, and I thought whenever we have a contrapositive, it is typically that answer choice that is correct b/c the LSAT writers like to make things as difficult as possible.

Have I gone wrong somewhere in my logic deduction? Please help!! Thanks!

[Jeremy Press]

Hi Shannon,

The first chain you drew is accurate, and so is your drawing of the contrapositive of that chain. The problem with answer choice D is that it actually reverses the first two elements of your (correctly drawn) contrapositive chain. Answer choice D states, "It is not safe to eat any fruit that is infected." "Any" is a sufficient condition indicator, thus answer choice D diagrams as: infected NOT safe to eat. This is the Mistaken Reversal of what you'd need to fill out your contrapositive chain, thus it cannot justify the reasoning in the stimulus. Make sense?

I hope this helps!

Jeremy

[lsatbossintraining]

Here’s my diagram using the double-not: could someone tell me where I’m going wrong?

Safe to Eat <—Inspected<—|—>Infected—>Rotten

s
Inferences: Safe to Eat<—>~Infected, ~Rotten

None of the answer choices seem to fit my inference or general diagram.

Thanks much.

[Adam Tyson]

You have diagrammed all the relationships correctly, boss, but you have to separate what is a premise (If inspected then not infected, and if infected then rotten) from what is a conclusion (if inspected then safe). We are looking for a new premise that will PROVE that if inspected, then safe, when all we know about inspected fruit is that it is not infected. The missing link is "and if it is not infected then it is safe." If we add that premise to the argument the conclusion becomes inescapable, proven...justified. That's what answer E does.

Your prephrase contains a double-arrow relationship (Safe Infected) that would do the job, although it's more than we need. We only need to know that any fruit that is not infected is safe - we do NOT need to know that any fruit that is safe is not infected. There could be some safe but infected fruit, as long as all the uninfected fruit is definitely safe. So, you had a perfectly good justify answer built in to your prephrase, but by looking for something stronger than was required you may have inadvertently rejected a perfectly acceptable answer choice.

[cking516_000]

Can anyone help me figure out why Infected --> Rotten is not being used to help justify the conclusion or is it?

[Adam Tyson]

It's not included, cking516_000, because it's not needed in order to justify the conclusion, and in fact it cannot be used to justify the conclusion because it can't be connected to the conclusion without making a false inference such as a Mistaken Negation. Basically, it's just there to cause confusion and make some wrong answers more attractive. Don't be distracted by it!

[dszhang]

Hello,

I completely understand why E is correct. However, I still find it difficult to understand why option B is irrelevant. Following the first premise, "any fruit that is infected is also rotten" (Inf -> Rot), shouldn't we be able to reach "~Rot -> ~Inf"? If it is not rotten, it is not infected. If it is uninfected, it is safe to eat. Then, isn't Option B essentially the same as Option E? Or am I doing something wrong with this extra step?

Your answer is greatly appreciated.

[Dave Killoran]

Hi D,

Up through this part you seem ok:

Following the first premise, "any fruit that is infected is also rotten" (Inf -> Rot), shouldn't we be able to reach "~Rot -> ~Inf"? If it is not rotten, it is not infected.

Where you seem to go wrong is:

If it is uninfected, it is safe to eat.

Ask yourself, where did you get this from? I suspect you may have misinterpreted (B) as saying: Safe Rotten in order to make this connection, but (B) is actually Rotten Safe (see the "any" there, which triggers the sufficient). Either way, the connection you are looking to make isn't there. If you want, post your reasoning on how you used (B) to get that statement and we can find the exact issue.

Please let me know if that helps. Thanks!