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

[dszhang]

Thank you, Dave,

I think you pointed out exactly my mistake, which was to read option B in reversal. Thank you so much for patiently explaining it to me! It makes total sense now.

[drewwellnitz]

Hello:

I have a very similar question to the one that dszhang asked last year. I fully understand why E is correct. However, I don´t understand why B is incorrect. In order to arrive at answer choice E, we established:
Inspected ➞ Not Infected
Inspected ➞ Safe to Eat.
Therefore,
Not Infected ➞ Safe to Eat
On the other side of the equation. We also established:
Infected ➞ Rotten
Not Rotten ➞ Not Infected
Therefore,
Not Rotten ➞ Not Infected ➞ Safe to Eat OR simply Not Rotten ➞ Safe to Eat (which is answer choice B).

[Jeff Wren]

Hi drew,

Based on your diagram, it's a little unclear what the premises of the argument are and what the conclusion is, so I'm going to rearrange them a bit for clarity.

Ignoring the first sentence in the stimulus for now, we have:

Premise: Inspected ➞ Not Infected
(Answer E, the missing Premise): Not Infected ➞ Safe to Eat
Conclusion: Inspected ➞ Safe to Eat

Answer E perfectly justifies the argument, as you noted.

Now let's look at the first sentence in the stimulus, which is:
Infected ➞ Rotten

And the contrapositive is:
Not Rotten ➞ Not Infected

Answer B is:
Not Rotten ➞ Safe to Eat

The problem is that this answer (when added to the other premises ) doesn't prove our conclusion that:

"Any fruit that was inspected is safe to eat" (my emphasis). We would need to link the "inspected" term to the "not rotten" term in order to draw this conclusion, which we can't do.

Currently, we have:
Not Rotten ➞ Not Infected

and we have:
Inspected ➞ Not Infected

But the "Not Rotten" and "Inspected" terms do not link together here as they are separate sufficient conditions. (One thing that makes this question so difficult is keeping track of the terms "inspected" and "infected" and not confusing them because they look/sound so similar.)

To give another example, imagine another argument.

If I'm in Texas, then I'm in the United States.
If I'm in Kansas, then I'm in the United States.

Therefore, If I'm in Texas, then I'm in Kansas.

As you can see, this logic is flawed. The two sufficient conditions cannot be linked here.