#24 - Any driver involved in an accident leading to personal

[Administrator]

Complete Question Explanation

Must Be True, SN. The correct answer choice is (B).

This is a complex conditional stimulus, with more than one way to diagram it, including the use of a "nested conditional." Some of these other options, including splitting the diagram into smaller sub-diagrams, are discussed further below in this thread. One approach is as follows:

(PI or >$500)

and Report

CR

(PI = personal injury happened in the accident; >$500 = more than that much in property damage happened; CR = capable of reporting)

That is, if there was either personal injury or more than $500 in damage, AND you are capable of reporting, then you must report.

The contrapositive is:

Report CR or (PI and >$500)

In other words, if you are not required to report, then EITHER you are incapable of doing so OR there was no personal injury AND there was not more than $500 in property damage.

Thus, if Ted is not required to report (the sufficient condition in the contrapositive above), then it must be true that either he is incapable of reporting the accident or else there was no personal injury resulting from his accident and any damage that resulted from it did not exceed $500. One of these possibilities is what we need to look for among the answer choices.

Answer choice (A): Ted being incapable of reporting would mean he was not required to report it, but it would tell us nothing about the amount of damages involved. This does not have to be true and is therefore a loser.

Answer choice (B): This is the correct answer choice. This matches our prephrase, in that damages in excess of $500 would require Ted to report the accident unless he was incapable of doing so, and since he is not required to report he must therefore be incapable.

Answer choice (C): The stimulus tells us nothing about who may be required to report an accident other than a driver, and it may be possible that nobody is required to report it. Perhaps all the drivers are incapable? Or perhaps there was no personal injury and the damages did not exceed $500? Ted not having to report proves nothing about anyone else involved.

Answer choice (D): This answer is essentially identical to answer A, with the additional problem that it focuses on injury specifically to Ted himself, whereas the stimulus would require a capable driver to report the accident if anyone, including someone other than himself, was injured. Ted being incapable proves nothing about anyone being injured, including Ted.

Answer choice (E): This answer is only one half or an either/or necessary condition, with the other half being "Ted is not capable of reporting the accident." It is not necessarily true that there was no personal injury or that there was not damage in excess of $500, as both of those things could have happened and it could still be the case that Ted is incapable of reporting and therefore not required to do so.

A challenging question to be sure, with a fairly complex multi-conditional relationship that uses both "and" and "or" on the same side of the diagram. Study and practice this one and you should be well prepared for similarly difficult questions in the future.

[mokkyukkyu]

Hi, I don't understand why E is wrong...is it because it does not take into consideration when BOTH of them happen?
How to diagram "unless" here?

thanks

[mokkyukkyu]

Or maybe...
(A or B) and C→D
Contrapositive:
Not D→not (A or B) OR not C
Not D

so B says IS B, so not C...
would IS B, not A be correct as well?

A=personal injury
B=property damage
C=capable to report
D=report is required

[Emily Haney-Caron]

Hi mokkyukkyu,

This one's definitely tricky. Rephrasing might help. If a driver is not required to report, then EITHER there was not property damage over $500 and no personal injury OR the driver is incapable of reporting OR BOTH. If there is EITHER property damage over $500 and/or personal injury AND the driver is capable of reporting, then the driver is required to report. Seems like that matches your diagram, basically. An answer choice that said "If there is property damage over $500, then there was no personal injury" would not be correct, because you could have property damage or personal injury or both and be required to report.

E is wrong because E is just saying one of the two you labeled A and B (personal injury and property damage) occurred; but if either occurred, even if it wasn't both, he would be required to report, unless he was incapable.

[bk1111]

Hi, I I understand why B is correct, but am still confused about why E is incorrect.

If Not Required -> (Incapable) or (Not exceed 500$ and Not Personal Injury), then why can E not be inferred from that?

Doesn't E just say If Not Required -> Not exceed 500$ and Not Personal Injury? and it is an OR statement, so either or both could be true?

[Jonathan Evans]

Hi, BK,

Let's do a bit of intermediate "translation" here between the information in the stimulus and the symbolization:

1. If someone's involved in an accident that causes more than $500 in property damage OR personal injury, then that person must report the accident.
2. The only way this person wouldn't have to report this $500+ damage/personal injury accident is if the person is incapable of doing so.
3. So, put these two statements together into one: If involved in accident with (more than $500 of damage OR personal injury) & capable of reporting accident, then must report accident.
4. Ted didn't have to report his accident.

What do you know about Ted? How's it possible he didn't have to report his accident? There are only two (three in a sense) ways possible that he didn't have to report his accident: EITHER there was not more than $500 damage AND NO personal injury OR he was incapable of reporting OR BOTH not more than $500 damage AND NO personal injury AND incapable.

Answer choice (B) hits this on the head: If more than $500, then must be incapable.

Answer choice (E) doesn't address the possibility that Ted was incapable of reporting the accident.

I hope this helps!

[freddythepup]

Hi, can you explain how you came to the conditional statement:

1) (PI or PD >$500) and CR --> RA

I read the nested conditionals discussion you had in another post and the example you posted there. Seems like the posted example was a bit different from this question and I understood that example better.

Here: I could only get to:
2) NOT (PI or D > $500 ---> RA) ---> CR

But I did not get the above conditional could become the first one. Any further explanation will be appreciated. Thanks!

[Adam Tyson]

I'm not sure how to interpret your conditional diagram, Freddy, but I think I would read it as "if it is not true that an accident involving personal injury or damages greater than $500 must be reported, then the driver involved must be capable of reporting it." That of course makes no sense - if the conditional claim is not true, and those conditions do not require reporting, then who cares whether someone is capable of reporting? I expect that is not what you meant with that diagram, so if this response ends up not helping, hit us up again.

Try this approach, without a conditional diagram. We know that Ted need not report the accident. But we know that if the accident involved personal injury, he would have to report it if he was able to. Also, if the accident involved damage to personal property greater than $500, he would have to report it if he was able to. So why doesn't he have to report it? There are a two options:

1. He isn't capable, in which case nothing else matters, he is off the hook

2. There was no personal injury AND there was not more than $500 in damages to personal property

So, what must be true? Either he is incapable, or he is capable but none of that other stuff happened.

Another way to deal with these complex conditionals is to break them into smaller rules. One rule is "If there is personal injury and the driver is capable, he must report", or:

PI
& RA
CR

The other is "if there is damage to personal property greater than $500 and the driver is capable, he must report", or:

D>$500
& RA
CR

Now you can deal with the contrapositives of both rules on their own with ease! Ted doesn't have to report, so per the first rule, either he is not capable of reporting or there was no personal injury, and per the second rule, either he is not capable of reporting or there was no damage to personal property greater than $500. That latter one proves answer B to be correct!

Nested conditionals are tough. If they aren't coming easily, break them into component pieces and handle them that way. Why make life difficult?

Keep at it, Freddy!

[haganskl]

Hello.
Is E wrong because of two reasons?

1. The statement includes an “or” instead of an “and”

&

2. It leaves out the nestled condition

If this AC was worded this way, would it have been correct?
Either no one was injured in the accident AND the accident
did not lead to property damage exceeding $500
OR Ted is incapable of making the report?

AC E says no PI OR no PD in excess of $500. Would
this still have been incorrect even if the
AC included the “OR Ted was incapable of making the
report?

Thanks!

[James Finch]

Hi Haganskl,

There are two possibilities that the stimulus sets up that would not require a driver in an accident to report it: either the damage didn't reach $500, in which case we wouldn't know whether they'd be required or not, or there was $500 in damage but the driver was incapable of reporting. As a Must be True question, we need 100% certainty; the second case is the only one that's certain, so it's the Prephrase that we need to go with. (B) matches this Prephrase perfectly, making it correct.

(E) does a sleight-of-hand with the language, where it switches "incapable" for "injured." These are not necessarily the same things, and can't be treated as such. It's wrong on this count, but also in that it still allows the possibility of the damage being less than $500: because we don't know what is or isn't required in that scenario, we can't make any inferences about it and thus can't attain the level of certainty needed for a Must be True question.

Hope this clears things up!