74 LR One Question 24
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Hello Dave
I wonder why you draw 500 & C. I though the reasoning is below;
capable -> report -> exceeding 500 driver
Not Report -> Ted
So, The answer is T -> not C.
I couldn't discover the point you drew 'and'.
Thank you
This one's tough; buckle up!
You can (as always) use our "unless stacking" method:
1. [$500 → R]
~C
2. → [$500 → R]
→ ~C
3. C → [$500 → R]
~[$500 → R] → ~C
In other words, if you're Capable of reporting, then if you cause $500 in damage, then you must Report.
By contrapositive, if you somehow do not have to Report, even though you did cause $500 in damages, then it must be that you weren't Capable of doing so.
Or, to put the whole thing more simply, If you're Capable and you cause $500 damage, then you must Report. If you can get out of Reporting, then either you aren't Capable of reporting, or else you didn't cause $500 in damage.
Dave. Your step three (3) in the “unless” stacking rule doesn’t read the same as how you explained in the contrapositive.
Specifically,
[~< 500$ —> ~ R] —> ~ C
= if not in excess of 500$ then if not have to report then not capable.
I don’t understand, how were you able to branch a separate sub contrapositive unless you meant
[~R -> ~ < 500$] -> ~C.
But then how do you also know where the “and/or” rule of contrapositive pairs applies? Mainly what stops me from saying “if not report or not <500$ then not capable = if capable then <500$ and must report.”
I may have answered my own question since B literally is the inferred contrapositive if ~R but <500$ then ~ capable.
Am I wrong ... please advise and thank you.
Your FACE doesn't read the same as how I explained in the contrapositive (SICK BURN).
I understand; this is really tough! But what I've written in both the video and in my comment above are two different and correct ways of saying the same thing.
Since you've asked only about the contrapositive, I'll start there (and let me know if you have more questions).
1. In my written comment, I've submitted that one entire conditional relationship (namely, that [$500 → R]) acts together as a unit to form the necessary condition within another conditional relationship (namely, C → [$500 → R]).
So in forming the contrapositive of the larger relationship, we need to completely negate the right hand side, just like we always do.
Thus, because the opposite of [$500 → R] is "NOT [$500 → R]," we form the contrapositive of "C → [$500 → R]" by writing "NOT [$500 →R] → NOT C."
2. Now, if you want to talk about negating an entire conditional relationship (not just one condition within the relationship), then you can do it like I've written in the preceding sentence and in the comment above, or you can negate it according to the following rule:
For any conditional "X → Y", the opposite of that conditional relationship is "X AND not-Y."
For example, if someone puts forward the untrue condition that To be in Boston, one must be in Texas, you point out their error by saying Nope. That relationship is not true. You can totally be in Boston AND not in Texas.
3. As to why the video is different than the written version, it's because I did in the video what seemed to me to be the easier way to understand the relationship. Notice that the video version (the one with the "and" in the Sufficient Condition) can always be transformed into the complicated version I've written in the comments.
For example, if it's true that anyone who is 7 feet tall and Athletic is good at Basketball, then I'd traditionally write: 7 + A → B. But you could also rejigger into the same meta-conditional I wrote above: 7 → [A → B]. See how this second version says "If a person is actually 7 feet tall, then if she's Athletic, she must be good at Basketball"? Or you could do it the other way, too: A → [7 → B].
If that makes your head spin, then maybe you see why I chose the symbolization I did in the video. I don't want your head to spin.
But to put a cap on it, let's leave with a firm rule: "For every sufficient conjunction (for example, X and Y → Z), you can correctly and differently symbolize as X → [Y → Z], OR ELSE as Y → [X → Z]."
Got it, I assumed that was the case but wanted to makes absolutely sure. And honestly that helps tremendously with other questions and games ... lol, and sick burn ... well played sir, and on my birthday no less.
Hope you had a great birthday (sick burns notwithstanding)!
Can someone please check my reasoning for AC E, Even if AC E said that no one was injured in the accident and the accident did not lead to property damage, it would still be wrong because it just affirms the necessary condition, right?
Capable→/Personal Injury and /$500
So, he could still be capable of reporting in which case that contradicts the premise that he is not required to report. Is that the right way to think about AC E?
If I'm understanding you correctly, then you got it.
I would have said it like this: (E) doesn't have to be true, because there are two ways to get out of reporting: (1) injury/property damage (more than $500), or (2) not being capable.
We know Ted doesn't have to report, so maybe (E) is true. Then again, maybe there was millions of dollars of mayhem, and Ted doesn't have to report because he's not capable of reporting.
why omit the personal injury aspect from the start? i know the ACs didnt mention it but was there another reason you didnt address it or was that the reason...
my intuition, bad btw, was to configure it as:
PI or 500+-> report unless incapable
...after that i wasnt sure where to attach the inverse of unless incapable, but i see you put it on the first part of the conditional w the 500+....would it also be right to express it as
PI + capable-> report..if the answers addressed Personal Injury instead of the damages...
1. Interesting question. If you watch closely (at 0:18), you'll see I didn't omit personal injury, but I think you and I read the first sentence differently. I'm not sure which one of us is correct.
I read it as "if the accident leads to personal injury exceeding $500 or property damage exceeding $500, then...."
And I see that you read it as "if it leads to any personal injury, or if it leads to property damage exceeding $500."
I see why you read it that way and I think it's a totally supportable position. I'd argue that the sentence in question is sloppy drafting.
2. I think that f you read my comments above this one, it'll answer your second question. But let me know if you still need help.