Setup and Rule Diagrams

[marissasalazar9899]

Hello, for question #12 I was confused as to how C is correct, because I thought C violated rule number 4. I was under the impression that T always needed to be placed between H and V. Is that not the case? Did i misunderstand the rule?

[Adam Tyson]

The thread for #12 is here, marissasalazar9899: viewtopic.php?f=1164&t=11241

Check that out for a full explanation of that question. You're right that T must be somewhere between H and V, but it doesn't have to be immediately between them. Answer C does have T somewhere after H and somewhere before V!

[npant120]

Hi smaani!

Rule #4 states "The table is auctioned on an earlier date than the harmonica or on an earlier date than the vase, but not both."

There are really two parts to this rule:
1.) T is earlier than H or V
2.) T is not earlier than both H and V

Based on this, we know that T must be earlier than either H or V, but not both.

With an "or" rule like this, one of the options must happen. So in this case we must have T earlier than H or V. If the rule did not include "but not both" then it would have left open the possibility that T was earlier than both H and V, but it still would have had to have been earlier than at least one of them.

Hope this helps!

Best,
Kelsey

Hello,

I want to make sure I am understanding this correctly. The way you chose your 3 templates was as follows: one was the V-T-H scenario and here you knew that H-L could not happen because that would force S into spot 1 so you knew L had to be 1st and all the other variables fall behind S. The other two templates were for the H-T-V scenario where in one template you had H-L, triggering the sufficient condition from the given rule and in the other template you had the sufficient condition not happening (aka L-H) and these two options cover all the possible scenarios for H-T-V. Is this correct? Or is there anything else to keep in mind. Also, would the way we approach the templates change at all if the rule that S can't be 1st didn't exist? I have a lot of trouble with the different scenarios we need to draw out when thinking about conditional rules (other than the sufficient happening and the necessary not happening), so just want to make sure I get this down right! Thank you

[Jeff Wren]

Hi npant120,

While I wouldn't want to speak for Kelsey, based on her templates, your assessment looks correct to me.

Another way to think of it is using templates for each of the combinations of (H - L) and (L - H) along with the combinations of (H - T - V) and (V - T - H), although only the 3 combinations listed work. As you correctly pointed out under the (V - T - H) branch, L must be ahead of H.

While the reason that you gave about forcing S into 1 is one way of thinking about it, that isn't the most direct way I would think about it. Once you know that only H or L can be first (a key inference definitely worth showing on your main diagram), you immediately know that L is first under the (V - T - H) branch. With L first, it is obviously ahead of H since first is ahead of everyone by definition.

Yes, in another game you may have consider another template if (H - L) were possible under the (V - T - H) branch.

[lemonade42]

Hello,
I'm confused on in the setup where it says rule 2 allows us to make this inference
"Allowed: M --- L --- H (this is also possible when H is not before L)"

If the rule is:
H - L ---> H and M are both before L
and the contrapositive of this is:
H and M are both after L ----> L - H
How would we able to get M --- L --- H from this rule? Because I can only see L being on the far right or far left, not the middle.

[Rachael Wilkenfeld]

Hi lemonade!

Great question. You've zeroed in on one of the tricky parts of contrapositives. What happens when we logically negate the term "both"?

Our rule says that if H is before L, then M is before L. That tells us that if H is before L, then both M and H are before L.
We need to find the logical opposite of "both M and H are before L." It's not "L is before both M and H." That's the polar opposite not the logical opposite. We need a statement that encompasses all the worlds in which M and H are not before L. We know there aren't ties.

So we need at least one of M or H to be after L. Our second conditional (L is before M, then L is before H and M) is triggered once L is before M. When M is after L, H is dragged along after too. But what happens when M is before L? The first conditional isn't triggered. Our second conditional isn't triggered. So we could have the situation M---L---H. It doesn't trigger our first conditional. It doesn't trigger our second conditional. It's compliant with the rules.

Hope that helps!