Diagram

[Carlystern]

The rules are:

M--->~O + ~P (P or O---->~M)
S--->P+T (~T or ~P--->~S)
W--->M+Y (~M or ~Y--->~W)

I ALWAYS have trouble with setting up the IN/OUT diagram without it looking completely cluttered. I just don't see it clearly. Any pointers for how to properly set up this diagram and maybe some hints to look for when I do it myself?

Carly

[ohthatpatrick]

Hey, Carly. Have you already read / learned about the Logic Chain in the Logic Games Strategy Guide?

The Logic Chain is that diagram in which we have two columns of matching letters and a bunch of arrows going between them and around them. If you haven't yet read / learned about this type of diagram, definitely check out the chapter on Open Conditional Grouping games (and if you have access to LSAT Interact, review the class 6 section on Games).

That method is a little different than what I can/will show you here. You should try to learn the Logic Chain because it's ultimately the most efficient way to handle these.

We can tweak your method, though, to be more effective.

As you're doing, you have to symbolize each rule and its contrapositive. Write the contrapositives underneath the original rule, not next to it. Try to line up all the arrows on your page so that the stack of conditional rules you have is very neat.

(I'll try to show you what I mean, but this typing environment ignores blank spaces, so I'll have to use a bunch of little periods to space things out correctly ... ignore the periods, they're just so that letters show up in the correct place)

1st pass through symbolizing the rules should leave you with:

.............M --> ~O and ~P
......O or P --> ~M
..............S --> P and T
.~P or ~T --> ~S
.............W --> M and Y
~M or ~Y --> ~W

Now what you do is go one-by-one:
1. Look at the idea(s) to the right of the arrow.
2. Ask yourself if that idea is any of the triggers on the right side of the arrow.
3. If you find one, then chain on that idea to the original conditional.

For example, the first line is
M --> ~O and ~P

I ask myself, "Does ~O or ~P ever trigger any of the other rules? Yes! ~P triggers ~S. Let me chain that onto the original".

Now my first line looks like
M --> ~O and ~P --> ~S

But you don't necessarily stop there. Now you ask yourself, "Does ~S trigger any of the rules? Hmmm, nope. Okay, this chain is done then. Onto the next one!"

We'll go through all six lines here and see if we can extend these conditionals by chaining any of them together.

Once we've looked through them all, our rules should look like this:

.............M --> ~O and ~P --> ~S
......O or P --> ~M --> ~W
..............S --> P and T --> ~M --> ~W
.~P or ~T --> ~S
.............W --> M and Y --> ~O and ~P --> ~S
~M or ~Y --> ~W

The Logic Chain I was telling you about will also help you find these chains (but it allows you to represent them even more efficiently).

Let me know if you have questions. Hope this helps.

[Carlystern]

Hey, Carly. Have you already read / learned about the Logic Chain in the Logic Games Strategy Guide?

The Logic Chain is that diagram in which we have two columns of matching letters and a bunch of arrows going between them and around them. If you haven't yet read / learned about this type of diagram, definitely check out the chapter on Open Conditional Grouping games (and if you have access to LSAT Interact, review the class 6 section on Games).

That method is a little different than what I can/will show you here. You should try to learn the Logic Chain because it's ultimately the most efficient way to handle these.

We can tweak your method, though, to be more effective.

As you're doing, you have to symbolize each rule and its contrapositive. Write the contrapositives underneath the original rule, not next to it. Try to line up all the arrows on your page so that the stack of conditional rules you have is very neat.

(I'll try to show you what I mean, but this typing environment ignores blank spaces, so I'll have to use a bunch of little periods to space things out correctly ... ignore the periods, they're just so that letters show up in the correct place)

1st pass through symbolizing the rules should leave you with:

.............M --> ~O and ~P
......O or P --> ~M
..............S --> P and T
.~P or ~T --> ~S
.............W --> M and Y
~M or ~Y --> ~W

Now what you do is go one-by-one:
1. Look at the idea(s) to the right of the arrow.
2. Ask yourself if that idea is any of the triggers on the right side of the arrow.
3. If you find one, then chain on that idea to the original conditional.

For example, the first line is
M --> ~O and ~P

I ask myself, "Does ~O or ~P ever trigger any of the other rules? Yes! ~P triggers ~S. Let me chain that onto the original".

Now my first line looks like
M --> ~O and ~P --> ~S

But you don't necessarily stop there. Now you ask yourself, "Does ~S trigger any of the rules? Hmmm, nope. Okay, this chain is done then. Onto the next one!"

We'll go through all six lines here and see if we can extend these conditionals by chaining any of them together.

Once we've looked through them all, our rules should look like this:

.............M --> ~O and ~P --> ~S
......O or P --> ~M --> ~W
..............S --> P and T --> ~M --> ~W
.~P or ~T --> ~S
.............W --> M and Y --> ~O and ~P --> ~S
~M or ~Y --> ~W

The Logic Chain I was telling you about will also help you find these chains (but it allows you to represent them even more efficiently).

Let me know if you have questions. Hope this helps.

Wow...yes, I've read that section, but the way you just explained it was amazing. I had an "ooooooh" moment. Thank you so much. This will help me out A LOT. Wow, thank you!

Carly

[ohthatpatrick]

Attached is a .pdf of a one-sheet explanation to this game. Let us know if you have any thoughts, suggestions, or questions about it.

[crf2132]

Question about this rule in the diagram" ............S --> P and T --> ~M --> ~W ". It seems to me that this would mean "T" would kick out "M" and therefore "W". However, isn't it possible to have T without S and that wouldn't trigger "~M"? It's the S that triggers the rule that "P-->~W", but not "T" by itself?

[ohthatpatrick]

I see where you're getting that from, but remember for the arrow to be triggered, the left side must be achieved.

If we're looking at
S --> P and T --> ~M --> ~W

We're not saying two separate thoughts,
S --> P
and
T --> ~M --> ~W

We're saying that the 2nd part of that chain is "P and T"
S --> P and T --> ~M --> ~W

So you can't trigger the --> ~M --> ~W stuff unless you have "P and T".

(Note: there are several ways to avoid this confusion, such as other diagrams, but if you're liking this sort of setup, just remember/try a couple things:
1. If this compound trigger continues to fool your eyes, consider writing it as S --> PT --> ~M --> ~W
2. If you're concerned about the implications of T being in, simply look at your leftmost column of triggers and find T.

If you do here, you'll see that T being in is simply NOT a trigger at all! (although T being out is a trigger)

.............M --> ~O and ~P
......O or P --> ~M
..............S --> P and T
.~P or ~T --> ~S
.............W --> M and Y
~M or ~Y --> ~W

When you're using this setup, you never need to dive into the chain halfway through. Any character who has any implications for other characters will show up as a trigger on the far left side.

So you don't go hunting for "T in" in the middle of chains, you simply look to see if there is a chain that starts with "T in".

Hope this helps.

[NatiO304]

Can someone please explain how you got the the MW/ POS placeholder inference? I got M/PO, but not MW/POS and am not seeing it. Any explanation would be appreciated!

[ohthatpatrick]

If you have an M / PO placeholder, you can ask yourself,
"When M is out, is anyone else forced out?
When P and O are out, is anyone else forced out?"

When M is out, W is out.
When P is out, S is out.

Since the M / PO placeholder is saying
"In any legal scenario, M is out, P and O are out, or both."
we can think
"In any legal scenario, M is out (which means W is also out), or P and O are out (which means S is also out), or both."

That's where the MW / POS would come from.

Hope this helps.

[JuanC212]

But for the W rule I thought we don't create placeholders when the arrows are remaining on one side of the LC? Since we don't necessarily know they have to be in/out.

My understanding is that we create placeholders when there is an at least one out (i.e. two arrows pointing out) or at least one in based on the conditional rules.

For example:

X --> not Y
y --> not X

At least one is out creating an X/Y placeholder in the out column.

Could you please clarify? Thank you!