#19 - Amy McConnell is considering running for election

[Administrator]

Complete Question Explanation

Cannot Be True—SN. The correct answer choice is (D)

Notice the word “If” that begins the second sentence. This is a clue to the fact that this question includes conditional reasoning. While it is not strictly necessary for you to draw a diagram in order to solve this question, doing so may help you if you answered it incorrectly.

If Lutz has a large campaign fund, McConnell will not run against him.

• Lutz LCF M RUN

If Lutz does not have a large campaign fund, McConnell will scrutinize Lutz’ record.

• Lutz LCF M Scrut. Rec.

These statements can now be put together by taking a contrapositive of the second statement, or

• M Scrut Rec. Lutz LCF

and “adding it on” to the first statement

• M Scrut Rec. Lutz LCF M RUN

If McConnell runs, that must mean that she has found something “dirty” in the record.

• M RUN Lutz Dirty

Finally, if Lutz’ record is clean, McConnell will not run.

• Lutz Dirty M RUN

which is a nothing more than a contrapositive of the previous statement.

Answer Choice (A): This can be diagrammed as:

• Lutz LCF and M RUN

Choice A implies that these two statements cannot coexist, or

• Lutz LCF M RUN

which is the same statement as

• Lutz LCF M RUN
  or
  M RUN Lutz LCF (by contrapositive).

Neither of these two statements, however, is found in our original diagram. Thus, there is no reason for us to assume that these two statements cannot coexist with one another.

Answer Choice (B): This choice can be diagrammed as follows:

• Lutz Dirty and M RUN

We have seen above that

• M RUN Lutz Dirty

so these two statements can definitely coexist in certain situations.

Answer choice (C): This can be diagrammed as:

• Lutz Dirty and M RUN

Using the explanation in choice (A) as your guide, you should be able to determine that in order for these two statements to not be able to coexist, the following must be true:

• Lutz Dirty M RUN

which is the same statement as

• Lutz Dirty M RUN
  or
  M RUN Lutz Dirty (by contrapositive)

Neither of these two statements, however, is found in our original diagram. Thus, there is no reason for us to assume that these two statements cannot coexist with one another.

Answer choice (D): This is the correct answer choice. It can be diagrammed as:

• Lutz Dirty and M RUN

Choice D implies that these two statements cannot coexist, or

• Lutz Dirty M RUN

which is the same statement as

• Lutz Dirty M RUN
  or
  M RUN Lutz Dirty (by contrapositive).

The latter statement is present in our diagram, which means that the two statements cannot coexist and choice D must therefore be false.

Answer choice (E): This can be diagrammed as:

• Lutz LCF and M RUN

We have seen above that

• Lutz LCF M RUN

so these two statements can definitely coexist in certain situations.

[scharles35]

So this was a conditional Cannot Be True question for the most part i got the question but i was stuck between answer choice (C) and (D). These two answer choices were very similar. I had ended up choosing answer choice (C) and someone help me understand why (D) is the better choice ?

[Lucas Moreau]

Hello, Charles,

This one is tricky - and so early on, too. The key is to diagram this question out into branches. The first branch is whether or not Lutz has a large campaign fund.

Lutz has a large campaign fund McConnell does not run
Lutz does not have a large campaign fund McConnell scrutinizes Lutz's record

Let's call the first outcome A, and the second one B. Now if we get to this second part B, McConnell scrutinizing Lutz's record, then it branches again.

McConnell finds hints of scandal McConnell runs
McConnell does not find hints of scandal McConnell does not run

Let's call that first outcome B1, and the second one B2. So, to recap:

A: McConnell does not run
B1: McConnell runs
B2: McConnell does not run

Answer choice C is not guaranteed to be false. If Lutz's record contains scandalous items, McConnell might very well find them, which would lead to outcome B1, McConnell running against Lutz. McConnell might not find those items, but McConnell seems tenacious to me.

Answer choice D, though, doesn't allow for any of the outcomes. If Lutz's record contains no hints of scandal, then McConnell cannot possibly find any, and so we are forced into outcome B2, McConnell does not run. But since the answer choice says Lutz's record is clean and McConnell runs, that is outside the rules of the question, and so it cannot be true.

Hope that helps,
Lucas Moreau

[scharles35]

Thank you Lucas this did help!!

[Basia W]

Good evening,

I was wondering if you could possibly explain how to deal with diagramming conditional statements such as "Lutz does not have a large campaign fund, and McConnell does not run against him" (a) using the double not arrows and the proper negations. I was slightly confused by the explanations in the book.

thank you,

best,

Basia

[David Boyle]

Good evening,

I was wondering if you could possibly explain how to deal with diagramming conditional statements such as "Lutz does not have a large campaign fund, and McConnell does not run against him" (a) using the double not arrows and the proper negations. I was slightly confused by the explanations in the book.

thank you,

best,

Basia

Hello Basia W,

Doing some diagramming:

1. LLCF (Lutz large campaign fund) MC slash R (McConnell doesn't run)
2. L slash LCF MC S (scrutinize)
3. LSC (Lutz scandal) MCR (assuming that "campaign for election" is synonymous with "run against Lutz", which seems fairly reasonable)
4. L slash S (Lutz has clean record, i.e., no scandal) MC slash R

So, answer D is correct, since diagram 4 above says that if Lutz is clean, McConnell doesn't run.
I'm not sure where double not arrows come in. The diagrams above seem sufficient. But if you want practice with double not arrows, you could make some up, e.g.,

4. L slash S (Lutz has clean record, i.e., no scandal) MCR. (I.e., you can't have Lutz being clean, and McConnell running, at the same time.)

Hope this helps,
David

[Basia W]

Hello,

thank you so much! I didn't want to use the double arrows either because I figured that would just complicate matters further (but the book explanation did for some reason). Thank you for your thorough and detailed explanation.

Best,

Basia

[Arindom]

Hi,

For this question, I picked C because I thought it violated the third conditional diagram. Could you explain why this is incorrect?

Thanks.

- Arindom

[Clay Cooper]

Hi Arindom,

Good question. I bet C was a popular incorrect answer choice.

Answer choice C does seem to violate the third conditional rule - until we remember to account for the first one. Remember that the first thing we were told was that if Lutz has a large campaign fund, Amy will not run against him - period. So it is possible that C is true: Lutz could have scandal on his record, but Amy would still not run against him if he has a large campaign fund.

Since C could be true, it is not the correct answer.

Hope that helps!

[Arindom]

Thanks, Cooper!

- Arindom