QUESTION TEXT: Any driver involved in an accident leading to…
QUESTION TYPE: Must be True
- (Injury OR $500) AND Capable –> Report
Report–> CapableOR ( InjuryAND $500)
- Ted doesn’t have to report the accident.
ANALYSIS: This question uses a compound sufficient condition (Injury OR $500). I’ll explain how to think about it with an example. You’re trying to prove someone can buy a sandwich. You can buy a sandwich if you have: A $20 bill OR a bunch of coins OR a credit card OR a gift certificate.
It doesn’t make sense to write all of those out in a conditional statement though. Really, it should be: money –> can buy sandwich
That simplified statement comes from your common sense knowledge that all of the above equal money. If someone asks specifics, you know that “money” is more detailed that what you’ve written, but you don’t need to write everything in the statement.
In the case of this question, the simplified statement would be:
Bad thing AND Capable –> Report
The contrapositive is:
Report –> Bad thing OR Capable
Basically, if you make a bad accident you have to report it – assuming you’re capable. The only catch is that “bad accident” has two components, either of which is enough to lead to a report.
“Unless” can be a tricky word to diagram. Use your common sense to think about what the word means. Making up examples to test the word is helpful.
For instance, go to work when you’re healthy unless there is a thunderstorm is: Healthy AND
thunderstorm –> go to work
You negate whatever is after unless and make it a sufficient condition.
Since Ted doesn’t have to report the accident, we can say that either he’s not capable, or the accident wasn’t bad. Which in this case means both conditions for bad are out: no injury, and less than $500.
- If Ted is incapable of reporting, then we have no condition that can force him to report. So we have no idea how bad the damage is.
- CORRECT. This is true. Normally, you have to report over $500 if you’re the driver. Ted doesn’t have to report, so he must not be capable. That’s the only exception to the rule.
- The stimulus only talks about the driver’s responsibility to report. Perhaps no other person ever has legal responsibility to report.
- There may be other reasons Ted is incapable of reporting. Perhaps he is far from any city, and he has no phone.
- This may not be true. It’s possible that someone was injured, but Ted is incapable of reporting. In that case, Ted doesn’t have to report.
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