#21 - If a mechanical aerator is installed in a fish pool

[wayouteast]

I got this question right, but it was more through feeling it out rather than knowing for certain. Was hoping to get some feedback as to whether or not my understanding of the stimulus is correct.

I was able to ascertain the flaw being an issue with conditional reasoning. We're given in the two sentences:
(1) (if aerator installed--> pool properly aerated) A-->B
(2) ~A
(therefore) ~B
Clearly a mistaken negation.

And then this is taken further in regards to the fish thriving where we see C-->B (if fish thrive-->properly aerated- from the contrapositive). If ~B is actually the case- the final conclusion is valid, but we can't ascertain that with the mistaken negation-so the final conclusion can't properly be drawn.

A: Matches this pretty well- I think. The only difference is unless instead of without.
B: different conditional structure.
C: ~A-->~B, ~A, therefore ~B.
D: Can't link the conditional statements into a chain.
E: Valid argument

Thanks!

[Dave Killoran]

You nailed it, congrats!

[Rachael Wilkenfeld]

Hi smrutibora,

Good analysis of the stimulus. We begin with a rule, a mistaken negation, and then another conditional attempting to draw from the mistaken negation.

If we reorder the stimulus, we end up with a structure like this:
A---->B
C---->B

John: Not A---->Not B
Since Not B---->
Conclusion: Not C

The error occurs in the mistaken negation, and we want to find that in our correct answer choice. The additional structural feature of C---->B is important to note as well, since this is a parallel flaw question and the overall structure is what matters here.

Let's take a look at those answer choices.

Answer choice (A) as you noted matches quite well. The change in terminology from "except" to "without" is structurally unimportant, as they have the same logical function as a necessary indicator.

If alum added---> brine replace water
Pickles crisp--->brine replace water

Paula: alum not added--->brine does not replace water
brine did not replace water---->
Conclusion: Pickles not crisp.

Answer choice (B) can be eliminated quickly because it does not have an additional conditional rule like our stimulus did. There's no C--->B, just the original statement, mistaken reversal, and a suggestion of how an individual should act.

Answer choice (C) also lacks the second conditional of C---->B, and can be eliminated for that reason.

Answer choice (D) is interesting. We have some similarities to the original.

If carrots covered ---> safely left in ground
if no frost damage---> carrots covered (or carrots not covered---->possible frost damage)

Even if we consider "frost damage" as a possible "C" condition, our conclusion in the answer choice is incorrect. Our conclusion is a correct application of the original conditional. Kevin covered his carrots, so they can be safely left in the ground. That conclusion is fine, therefore, answer choice (D) is incorrect.

Answer choice (E) is the one that seemed to look tempting to you. A big problem here is in the phrasing of the original conditional.

If tomatoes are not stored in a dark place----> seeds SOMETIMES sprout.

Oof. That sometimes there really throws us for a loop. We can't say for certain that they will sprout, just that they sometimes sprout. The conditional logic changes with that word "sometimes" in there, and since we didn't see that in our original conditional, we can eliminate the answer choice right here.

Overall even though it looked like it might be a time consuming or complex problem, the additional C---B rule in the stimulus helped us to quickly eliminate 2 wrong answer choices. That's a win every time.

Good analysis again smrutibora!