Biconditional Rule Interpretation Question

[shaorahman]

Hi All,

I was going through the solutions on the Getting Familiar game for Ch. 6, Mismatch Ordering. Here is the scenario, and my questions below:

Doctor X will see exactly five of seven patients- K, L, M, N, O, P, and Q- that are all waiting in the lobby. She will see these patients one at a time and in order. The following conditions apply:

She will see both K and M, and she will see K before M.
If she does not see O, she will see P. Do we know we must have both because it doesn't tell us otherwise? I read this as mutually exclusive..
-O --> P
-P --> O

She will see Q or P, but not both. Simple enough. I know one of them will be in and the other one out
If she sees either L or O, she will see them after M.
If she sees N, she must see N first.

So, the solution proceeded to link up some rules, and the one I cannot understand is this: -P-->O<-->M--O
Why is it a double headed arrow? I get O-->M--O, but not the other head. When was it ever indicated that if M is in O must be in too?

Thanks!

[ohthatpatrick]

Hey, sorry for the slow reply. Sometimes posts accidentally fall through the cracks, as yours did.

You wrote:
If she does not see O, she will see P. Do we know we must have both because it doesn't tell us otherwise? I read this as mutually exclusive..
-O --> P
-P --> O

You should NOT read that as mutually exclusive.

What happens if O and P are both In? Does it break the rule?

The rule says "If O is out ..."
Okay. Stop reading. O is not out, so this rule has no meaning to us.
We can't break a conditional rule unless we first trigger the left side idea.

People naturally "see" those rules as suggesting mutual exclusivity, but they don't.

When we see
-O --> P
-P --> O

It's telling us "O and P cannot BOTH be out."

But they could both be in. And we could rephrase "can't both be out" into "at least one is in". That's why we're going to put a P/O placeholder in the IN column.

I'm confused / concerned by the notion of "Do we know ____ because it doesn't tell us otherwise".

We only know what they tell us. We can't make assumptions otherwise. That's kinda like saying in an Ordering game "Do we know that G is always 3rd because it doesn't tell us otherwise?"

O and P could both be in, but only one of them HAS to be in.

In terms of the double arrow notation in the book, it was kinda dumb/lame.

All the double arrow is showing is
M - O --> O

You seemed to be interpreting it more narrowly as "M --> O", but it was the idea (M - O)

The only reason they made that a double arrow is that
IF M - O, then I guess O must be in.

It was silly to write it that way in my opinion, though accurate.

Let me know if you're still confused by any of this.

[VendelaG465]

I'm finding it a bit difficult to wrap my head around the " If she does not see O, she will see P" rule. I understand how at least one of them HAS to be in, but how can both[i][/i] be in if -O --> P & -P ---> O we're forced to pick either or. Is it because it wasn't specifically mentioned "but not both" as the next Q/P rule therefore leaving the "both in" possibility ?

[VendelaG465]

one more question as well for Q5 since M is fourth how do we know L/O go in 5th? The 4th rule states L----> M-L & O----> M-O but how can we make that inference when #5 is only saying M is fourth ? the L/O rule wasn't triggered. I was tempted to read it that way but figured we didn't know for sure if L or O was in so we couldn't infer anything.

[obobob]

Hi, does anyone know where the question set is from? Like which past exam with section number and question numbers?

[ohthatpatrick]

It's not from an exam, or else there would be numbers listed.

When you don't see stuff like PT ___ , Sec ____, Q ____ , then you know it's just a game we made up for the sake of the book.