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?
#24 - Any driver involved in an accident leading to personal
(A or B) and C→D
Not D→not (A or B) OR not C
so B says IS B, so not C...
would IS B, not A be correct as well?
C=capable to report
D=report is required
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 $500, then there was no personal injury" would not be correct, because you could have property damage or personal injury or both and be required to report.
E is wrong because E is just saying one of the two you labeled A and B (personal injury and property damage) occurred; but if either occurred, even if it wasn't both, he would be required to report, unless he was incapable.
Hi, I I understand why B is correct, but am still confused about why E is incorrect.
If Not Required -> (Incapable) or (Not exceed 500$ 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?
Let's do a bit of intermediate "translation" here between the information in the stimulus and the symbolization:
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 less than $500 damage AND NO personal injury OR he was incapable of reporting OR BOTH less than $500 damage AND NO personal injury AND incapable.
Answer choice (B) hits this on the head: If less 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!
Could you show me how you would diagram this?
There's more than one way to diagram this one, mankariousc, but I'll share one with you here using the same approach that Emily used in her prior response:
(PI or $500)
(PI = personal injury happened in the accident, $500 = at least that much in property damage happened, CR = capable of reporting)
That is, if there was either personal injury or at least $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 at least $500 in property damage.
There is another, more complex way to do this using "nested" conditional statements, and you should feel free to look those up in our blog and in other threads in this forum, but this approach worked well for me and so I didn't bother with the nested approach. It appears that my colleagues here felt the same way, as none of them used the nesting approach either. Keep it simple - that's my motto on this test!
I hope that helped!
Adam M. Tyson
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The explanations for "B" being correct still don't make sense to me. Why does Ted's car being damaged in excess of $500 mean he is incapable of reporting the accident? Further, all the Powerscore commenters changed "exceeding $500 in damage" from the stimulus to "at least $500 in damage" in their answers, so maybe the explanations are wrong due to this misreading of the stimulus.
Just so I understand this correctly:
(P1) "Any driver involved in an accident leading to personal injury or property damage exceeding $500 is legally required to report the accident to the department of motor vehicles, unless the driver is incapable of doing so". Diagram: Personal injury or property damage exceeding $500 and capable of reporting--->must report. (contrapositive: must not report---> no personal injury and no property damage exceeding $500 or not capable or reporting).
(C) "Ted is not required to report the accident in which he was involved as a driver".
As a prephase, this conclusion statement allows the inference in "E" by using the contrapositive above (that is, if "E" was an "and" statement and not an "either/or" statement). Ted wasn't required to report because:
(1) there was no personal injury AND no property damage exceeding $500 that both occurred
(2) Ted was incapable of reporting (presumably due to his own injuries)
(3) there was no personal injury AND no property damage exceeding $500 AND Ted was incapable of reporting (presumably due to his own injuries). Basically both parts of the contrapositive were present for this answer to be true.
"B" states that "if Ted's car was damaged in excess of $500 in the accident, then he is incapable of reporting the accident to the department of motor vehicles". However, why is Ted's car damage exceeding $500 in the accident sufficient evidence that Ted is incapable of reporting the accident? I thought that Ted's excess damage of $500 meant he had to report the accident, unless he wasn't capable of doing so. Couldn't Ted have endured over $500 in damage and still be able to report the accident (and actually be required to do so)? Why is an excess of $500 in damage equated with an inability to report?
I could see answer "B" being correct if you add the conclusion to "B" like this: If Ted's car was damaged in excess of $500 in the accident and (C) Ted is not required to report the accident, then this lack of requirement is due to the fact that he is incapable of reporting the accident.
Is this how the answer is arrived at? I'm sorry, I'm just terribly confused. Thanks for any clarification!
Just to help a bit here, I'm not seeing that they did that. In fact, the first couple of PS commenters were exact about using the phrase or the negation (when appropriate) and Adam appears to simply have used "$500" as notation for the same idea (which is perfectly fine as notation). So, I'm not seeing any issues there, and the explanations are actually spot on.
The more likely source of difficulty for you is that this is just a hard problem with multiple pieces. Without worrying for a moment about what the answers say, let's instead focus on what you know if you don't have to report the accident. All the PS instructors discussed this correctly, but let's just hit it one more time for clarity's sake. In this case, when you don't have to report the accident, at least one of the following occurred:
How do we know this is one of the options? From the contrapositive of the conditional relationship given in the first half of the first sentence:
OR Report Accident
When you reverse and negate the terms, it appears as:
Report Accident +
2. Driver Incapacitated
How do we know this? From the "unless" portion of the first sentence. This is actually the tricky part here, because it is, as Adam noted, a nested conditional. Essentially, it means that if the first half did NOT happen (which we know since the accident did not have to be reported), then the remainder of the sentence ("the driver is incapable of doing so") has to occur.
Thus, from the fact that Ted doesn't have to report the accident, we know that at least one of the following occurred:
2. Driver Incapacitated
So, that by itself is complicated to determine! From there, the answers don't make life much easier, which is primarily the case because we are still dealing with multiple possible outcomes. Just keep in mind that at least one of the two above has to occur (meaning if #1 doesn't occur, then #2 must occur, and if #2 doesn't occur, then #1 must occur).
Answer choice (B): If Ted's care was damaged in excess of $500 (Meaning this occurs: >$500 Damage), then option #1 above does not occur. That forces option #2 to occur, meaning that the Ted was incapacitated. This is exactly what (B) says (if #1 didn't occur then #2 must occur), and thus (B) is correct.
Answer choice (E): You might already see the problem here, which is that this only addresses one side of the possibilities and says nothing about the Driver Incapacitation side. As such, it doesn't have to be that either of these two things occurred.
Overall, this is a complicated problem, and the conditional relationships can be represented in different ways depending on what's easiest for you. Since the forum doesn't give us the best tools to display the different diagrams, I may try to make a video on this and explain it that way. It's certainly the type of problem that is worth a longer, more involved explanation.
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In answer choice (A), it's not the case that both conditions are being met. The prompt gives us two reasons why a driver doesn't need to report an accident, either (1) the accident didn't incur $500 in damage, or (2) the driver is incapable of reporting the accident (or both).
We know that Ted doesn't have to report the accident. So we know that either he didn't cause $500+ in damage, or he's incapable of reporting, or both.
Answer choice (A) states that if condition #2 happens, it is because condition #1 happened.
That's not necessarily the case. If Ted is incapable of reporting the accident, he is not required to report it, regardless of how much damage the accident caused. We don't know, based on the prompt, whether Ted was in a low-damage accident or not. We cannot infer that the accident was minor (under $500) just based on the fact that Ted doesn't have to report it.
I hope that makes sense. Good luck studying!