Q20

[BlossomB913]

I'm confused about #20. I get why E must be true but it looks to me like B must be true also.

I have 3 frames. The only one with M first has M-F-G-K, M and M-H-L with H before G (I wish I could draw it).

Since H is before L in that frame then it would have to be second.

Can someone help me see what i did wrong with my framing?

[ohthatpatrick]

If you're confused about (B), try ignoring your frames for a sec and trying to figure out if you can build a legal scenario that contradicts (B).

we're given M _ L _ _ _
and we want to contradict (B), so we want to avoid putting H in spot 2.

Where else can we try putting H?
Because the first two rules give us H - G - K, we could only put H in 2 or 4.

So let's put it in 4,
M _ L H _ _

Putting H in 4 forces G and K to follow in the final two
M _ L H G K

Who's left? F. Let's put him in spot 2 and see if we've broken any rules.

M F L H G K

As I go down all four rules, I see I'm in compliance!

How did you end up with 3 frames, I wonder.

We could create two frames for the 3rd rule (the trigger does or doesn't happen)
i. F - M
ii. M - F

We could create two frames for the 4th rule (M is either before both H and K, or after both H and K)
i. M - (H, K)
ii. (H, K) - M

If you wanted to combine those, you'd get four frames (which sounds like too much),
because you'd have to do
F - M .... with M - (H, K)
F - M .... with (H, K) - M
M - F .... with M - (H, K)
M - F .... with (H, K) - M

Normally when a relative ordering game gives us TWO different rules that each present an either / or, rather than doing four frames (too much) or zero frames (too little), we just pick ONE of those either/ors to frame, and let the other either/or rule just still hang in uncertainty.

I would probably make two frames, using the last rule, and then I would just have to still play around with the uncertainty of whether F - M or not (i.e. with whether I need to worry about that conditional rule)

[BeverlyD396]

I think for this question, what is throwing me off is the the rule that if F-M -> L-H

This lead me to think of the contrapositive as a rule/truth, which would be: H-L -> M-F

This is why I was lead to be live that B must be true, because of the contrapositive. Was this the wrong brain-road to go down?

[ohthatpatrick]

Hey, there. Sorry for the non-response. This post slipped through the cracks until now.

You are correct to think about the contrapositive the way you said:
F-M -> L-H
H-L -> M-F

When the question tells us that M is 1 and L is 3,
M _ L _ _ _
have we triggered either one of those rules?

Do we know whether F is before M? Yes, we know that F is not before M. That means that there IS no rule.

Whenever the trigger isn't happening, a conditional rule is meaningless. If the trigger doesn't apply to a given situation, then the rule has nothing to say.

You could also look at the contrapositive version, but you don't need to. Knowing the rule doesn't apply from the original means that we don't have to worry about the contrapositive.

If we did look, we'd ask ourselves, "Do I know whether H is before L?"

We don't. H could be earlier, could be later.

I think you started interpreting the rule / contrapositive as an either/or, as though you were always bound to have one or the other triggered, but that's not how conditionals work.

If I say
"If you're in Los Angeles, you're in California", we get
LA -> CA
and
~CA -> ~LA

Were we to learn that "Sammy is not in LA", we know the trigger on the original rule doesn't apply. But that doesn't tell us anything about whether or not Sammy is in CA. We can't suddenly switch to thinking that the contrapositive is happening.

Hope this helps.