I don't know if this is the right place to post this. But I have a question about rule notation for "Drill it: Grouping with Mismatch" on page 564 of LG Strategy Guide.
One of the rules is "Unless O is used in the same cookie as K, it is used in the same cookie as L."
The solution in the guide notates this rule as (in drawing): OL (In a box cross out) ---> OK (In a box)
But I thought it should instead be: OK (In a box crossed out) ---> OL (In a box)
Can someone please explain to me why I'm wrong?
Also, the solution suggests to make frames for this question assuming O is selected and uses them to solve question 2. But how is this reliable when there are more elements (8) than available slots (6)? Isn't it possible that O is not selected in the first place?
To counter answer choice A of question 2, I came up with: P, T, O and M, S, L selected for each cookie... but yet from the frames A is the answer..
Can you please explain this question once again?
Thank you in advance!
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Re: LG Strategy guide mismatch
The way you symbolized it is identical in meaning to the way they symbolized it, so you both got it right. 
They said
~OL --> OK
You said
~OK --> OL
The way you wrote it is the contrapositive of how they wrote it (or vice versa). When we write the contrapositive to a rule, we haven't changed the rule in any sense. We've only allowed ourselves a different way to see it.
Which way you write it is completely arbitrary, so there's no right or wrong way to right a rule.
Many students (including me) contrapose almost every conditional rule we write, so that we have both ways of looking at the rule. And when it comes to In/Out thinking, writing the contrapositive of a rule can sometimes alert us to potential placeholder inferences.
By looking at
~OL --> OK
~OK --> OL
I see that O will always have to be with K or L (or both). If it's not with one of them, it has to be with the other. This also means that there's no way for O to be out.
If O were out, then we could say that "O is not used with L", or ~OL, so we would trigger the requirement that (O is used with K).
That was a contradiction: "If O is out ....... then O is used with K". That's one way of seeing that O can never be OUT. More simply, when I look at that pair of conditional rules, I can see that O will never be out, because throwing O out would trigger both versions of that rule!
This would answer your question about why the frames are assuming that O is always in. O is always in, because putting O out would contradict the 4th rule.
In terms of Q2, the scenario you came up with as a counterexample for (A) was
PTO | MSL
but you're breaking the 4th rule. Since O isn't being used in the same cookie as K, the rule tells us that O must be used in the same cookie as L. But you don't have O being used with either K or L.
In every scenario of the game, O will be with K or L.
If I said "Unless Paul is sick, he will come to the party", we know for sure that at least one of those two things will happen.
He's either sick, coming to the party, or both.
Similarly, rule 4 guarantees to us that O is with K, O is with L, or both.
(rule 3 makes it impossible for O to be with K and L, since N would also have to come along for the ride, but the logic of rule 4 itself allows for OKL to all be together)
Hope this helps.
They said
~OL --> OK
You said
~OK --> OL
The way you wrote it is the contrapositive of how they wrote it (or vice versa). When we write the contrapositive to a rule, we haven't changed the rule in any sense. We've only allowed ourselves a different way to see it.
Which way you write it is completely arbitrary, so there's no right or wrong way to right a rule.
Many students (including me) contrapose almost every conditional rule we write, so that we have both ways of looking at the rule. And when it comes to In/Out thinking, writing the contrapositive of a rule can sometimes alert us to potential placeholder inferences.
By looking at
~OL --> OK
~OK --> OL
I see that O will always have to be with K or L (or both). If it's not with one of them, it has to be with the other. This also means that there's no way for O to be out.
If O were out, then we could say that "O is not used with L", or ~OL, so we would trigger the requirement that (O is used with K).
That was a contradiction: "If O is out ....... then O is used with K". That's one way of seeing that O can never be OUT. More simply, when I look at that pair of conditional rules, I can see that O will never be out, because throwing O out would trigger both versions of that rule!
This would answer your question about why the frames are assuming that O is always in. O is always in, because putting O out would contradict the 4th rule.
In terms of Q2, the scenario you came up with as a counterexample for (A) was
PTO | MSL
but you're breaking the 4th rule. Since O isn't being used in the same cookie as K, the rule tells us that O must be used in the same cookie as L. But you don't have O being used with either K or L.
In every scenario of the game, O will be with K or L.
If I said "Unless Paul is sick, he will come to the party", we know for sure that at least one of those two things will happen.
He's either sick, coming to the party, or both.
Similarly, rule 4 guarantees to us that O is with K, O is with L, or both.
(rule 3 makes it impossible for O to be with K and L, since N would also have to come along for the ride, but the logic of rule 4 itself allows for OKL to all be together)
Hope this helps.
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