Must Pick Either X or Y, but not both!

[chike_eze]

Quick question: What is the difference between..
(1) Shelly must pick either X or Y, but not both
(2) Shelly picks either X or Y, but not both

Please diagram both statements.

[noah]

I don't see any difference.

And, as for diagramming those, it would depend on the game type.

[chike_eze]

@Noah,

So would the following be accurate

X --> not Y

or would you go as far as

X <--> not Y for any one of them?

I think my confusion with "must" in the first statement is that I read it as implying that we must pick one, i.e., we cannot have both X and Y out. In the second statement, I read it as both X and Y could be out, but if one is picked then the other can't be picked.

Let me know if this makes sense. (LSAT you are driving me crazy! I hear myself speaking and I'm like... What??)

[noah]

Since both rules indicate that she'll pick one of them, for binary games, this would be X <--> - Y, and Y <--> X.

You might be thinking of the difference between these two rules:

1) Mary cannot pick both X and Y.

2) Mary picks either X or Y but not both.

Here's how these translate:

1) X --> - Y

2) X <--> - Y

(and contrapositives)

The LSAT is a wicked test! Maybe time to take a day off, get some exercise and let your brain rest. It won't work to push and push all the way to game day...

[hilarykustoff]

I'm still really confused with this. I don't see the difference.

[timmydoeslsat]

The ultimate answer to the initial poster's question is that it does not matter if the word must is included in an either or situation, as it is already implied by stating either or.

The issue of either or can be seen as this:

You are to always recognize that both possibilities in the either or context can occur. You will be explicitly told "not both" if it is the case that both will not happen together.

To state either A or B, it is not necessary for me to say "or both" - as this is implied in the statement. Saying Either A or B automatically entails me to believe that both can happen.

However, if I said "Either A or B, but not both." - this is telling me that one will be picked and one will not be picked.

There is no way that I could not pick on, as I am told either A or B. And there is also no way that I could pick both, as I am told not both.

Of course, there are times when you have a situation like the following: Either you drink water or you do not drink water."

It is not necessary for me to state but not both, as these things are automatically mutually exclusive. There is no way to be both.

[hilarykustoff]

Thanks for your help!

Do you think you could show me the diagrams? I keep getting confused when diagramming the constraints for the binary games. I never know which ones go two ways and which ones don't. I'm just so confused on all the tricky diagramming for orientation questions.

[timmydoeslsat]

If I were given the statement Either A or B:

I would simply write A or B

If I were given the statement: Either A or B, but not both:

I would simply write 1 A/B in, 1/A/B out.

The above posts are making use of the idea of biconditionality, which is the idea that a condition is both necessary and sufficient for another condition, typically framed in a manner like "if and only if."

A if and only if B.

You are familiar with the idea of "if" introducing a sufficient condition and "only if" introducing a necessary condition. When you have a situation of both being presented, we can represent that with a two-way arrow.

A <---> B

The presence of A will guarantee the presence of B and vice versa.

We also know that if we do not have A, we will not have B. Vice versa, in that if we do not have B, we will not have A.


The idea of biconditionality is absolutely valid in a situation of "Either A or B, but both" situation.

You simply choose one of the variables and negate ONE.

~A <----> B

We know that if we do not have A, we will have to have B, as we have to pick one. We also know that if we B, we will not have A, we can simply follow the 2-way arrow.

What is great about the biconditional arrow is that once you negate one side of it, you negate the other side.

So if you do HAVE A, you necessarily do NOT have B.

And this is all consistent with the idea of Either or but not both.

If you are given a situation of strictly Either or:

You can do this: ~A ---> B

This is simply showing that at least one must occur.

[hilarykustoff]

Sorry I'm still slightly confused. I can't grasp this topic.

1. Either A or B looks like: A-->-B and -A-->B
2. Either A or B but not both: -A<-->B and A<-->-B

I guess I'm looking how to diagram these conditionals for in and out games.

[timmydoeslsat]

Sorry I'm still slightly confused. I can't grasp this topic.

1. Either A or B looks like: A-->-B and -A-->B
2. Either A or B but not both: -A<-->B and A<-->-B

I guess I'm looking how to diagram these conditionals for in and out games.

Well, for in/out games, if you were told A ---> B or C

Simply leave it at that!

Do not go into this unnecessary conditional work.

You know that once you place A, at least one of B or C will follow.

That would be an unusual rule for an in/out game though, with that form of a necessary condition.

Having the "or" in a necessary condition on a logic game is going to cause a lot of problems, as you have three options: Just B, Just C, or both B and C.

If it were the case that the test writer placed a conditional like that, expect to have local questions that will have denied the possibility of say, variable, B. In which case, if you had A, you must have C since B is out.

Usually you will see the "or" component be something like:

A or B ---> C



As for the concerns you directly addressed:

1. Either A or B looks like: A-->-B and -A-->B
2. Either A or B but not both: -A<-->B and A<-->-B

In #1, the first conditional, that does not have to be true. If you have A, you could still have B.

Your second conditional is correct, as the absence of one variable in an either or scenario will have the presence of the other variable.

Your 2. statement is correct, however you can just choose one, those are the exact same, just contrapositives of each other.

[noah]

I was about to post, but I think the last part of Tim's last post clears it up. (Thanks, Tim) Tell me if you're still unclear, Hilary.

[RyanT361]

Hello,

I have a follow up question regarding this topic. On Page 347 of the Logic Games book, there's the "Either Orion or Nimbler is sold at auction, but not both". This is the "Horse Breeding" game.

I'm still not sure as to why there's two version of the rule. I understand one version of it: O-----> -N and the contrapositive: N---->-O, but why the second part: -O---> N and the contrapositive: -N----->O?

I thought that the first display (O---->-N) would satisfy the rule, as If you select O, N is out and vice-versa via the contrapositive. I just don't understand the significance of -N------>O.

Please help!

Thanks in advance!

Ryan

[ohthatpatrick]

So, say we only have the rule that
O --> ~N
N --> ~O

Would that rule be broken with this scenario?

Sold:
Not Sold: O, N

Nope, this scenario is fine. Our rules say, "If O is sold", but in this scenario it isn't, so that rule has no bearing.
And our rules say "If N is sold", but in this scenario it isn't, so that rule has no bearing.


Say we only have the rule that "Either Orion or Nimbler is sold at auction, but not both".

Would that rule be broken with this scenario?

Sold:
Not Sold: O, N

Of course! We're breaking the requirement that one of them needs to be sold.

The rule you were thinking of, (O --> ~N, and N --> ~O), would effectively keep them from both being sold.
But that rule has no power to prevent them from both being not sold, because putting O or N in the out column doesn't trigger that rule.

We can adapt the conditional rule to be biconditional:
O <---> ~N
~O <---> N

This captures the idea that as soon as you put either letter IN or OUT, it automatically triggers the other letter to be in the opposite group.

Or you can treat biconditionals ("but not both") as an either/or:
O, ~N or ~O, N

Or, you can just immediately divide them up, putting a placeholder for one of them IN and one of them OUT:

Sold: O/N
Not sold: N/O


Hope this helps

[RyanT361]

Thank you Patrick, so if I understand correctly, displaying the biconditional 1) N<-----> ~O and 2) ~O<---->N would satisfy the rule as if the trigger is not there, and you only have one rule displayed, then you are only allowing for the possibility of one outcome, i.e. only O could not be picked, whereas if you have both conditionals (1 and 2), then you are correctly displaying the rule, which would mean one of them must be in (not both of them), and both of the can't be out.


How does this rule compare to negative sufficient condition rule, in grouping in/out games? I find myself getting confused with rules such as:

"When A is not selected, then B s selected". This would diagram as; ~A-----> B

Which would mean rhat atleast one of them must be in at any time, and both can't be out, but it doesn't discount the possibility that in a grouping in/out game that both of them could be in, correct?

Then in Violin in/out grouping game on page 376 of the LG book, there's a rule:
"If U is not selected then H is selected".

Wouldn't this mean that one of them is at least always in "U/H"? But then on page 379, there's a display that atleast one of them is always out, I thought that based on a negative sufficient rule, that there could be a possibility that both of them could be in?

Does it have to do with the specific wording of the individual game (e.g. both of them can't go twice, or something to that effect?) I'm not sure why there seems to be a difference, is there some nuance that I should be looking for with in/out grouping games when it comes to either/or questions?

Another example of this is the Bird watching game on PT 33 (S4, Game 2), they have a rule where if J is out, s must be in ~J----->S, where both J and S could be in.

Thank you for your help!

Ryan

[ohthatpatrick]

The exception you're looking at there is a typo. It's in the Errata:
https://www.manhattanprep.com/lsat/erra ... es-5th-ed/

If you have a rule that's like
A --> ~B
B --> ~A

then at least one is OUT (both of them could be out)

If you have a rule that's like
~A --> B
~B --> A

then at least one is IN (both of them could be in)

There aren't any exceptions to that, although other factors in a game could combine with the effect of one of these rules to yield a situation in which it's always the case that one is in, one is out.

I'm not sure I understood you here:
so if I understand correctly, displaying the biconditional 1) N<-----> ~O and 2) ~O<---->N would satisfy the rule as if the trigger is not there, and you only have one rule displayed, then you are only allowing for the possibility of one outcome, i.e. only O could not be picked, whereas if you have both conditionals (1 and 2), then you are correctly displaying the rule, which would mean one of them must be in (not both of them), and both of the can't be out.


Any time we have a normal conditional rule, we never NEED to write a contrapositive for its effects to still be a mandatory constraint on the game. We just write the contrapositive to assist our brain in seeing two different ways a given rule could be triggered.

If you have a bi-conditional, it's not really a conditional rule. It's just an either/or situation. We can choose to write it conditionally if we want (I do not), in which case you'd need to write both versions or else you're only showing yourself half of the either/or. Or you can just drop the arrows altogether and write out the two possible worlds created by the either/or.

[RyanT361]

Thanks again Patrick.

For bi-conditional questions, what verbiage (or game rules) indicates that it is indeed bi-conditional? I seem to have trouble discerning when an in/out grouping game rule is bi-conditional and when its just conditional.

For example: PT 41 S2, G3 (p. 384 of the LG book) (The board of directors) has two bi-conditional rules (W serves on a different committee than Z, and U serves on a different committee than G) these two I clearly understand (it makes sense as well since they would each trigger each other).

However, on the Practice Game 2 on P. 553 of the LG handbook, there's two conditional rules, that at least to me, look very similar to a bi-conditional rule "G and J cannot both be selected" and "H and O cannot both be selected." This to me, looks like the rule in the previous game above, where they have to serve on different committed. They haven't indicated which one could be in or which one could be out. Or am I looking for some wording that indicates that they would both have to be selected, like in the PT 41 game, all the elements are in, whereas in the practice game, only 5 of 9 will be in, so there's a chance that they may not even be picked at all -- does this prevent it from being bi-conditional?

Can someone please help me see the light with this please?

Thank you,

Ryan

[ohthatpatrick]

Bi-conditionals usually have a signature ring:
if and only if
if but only if
then and only then
when and only when

The two part rhythm is reminding you that we were given a sufficient condition and a necessary condition.

For the grouping game rules that may or may not be bi-conditional, you're essentially just asking yourself whether two people can EVER be found in the same place.

W serves on a diff committee than U - okay, that's bi-conditional because they can never be found in the same place

W and U cannot both be selected - that's just saying they can't be IN together. They could both be rejected. So it's not bi-conditional.

[AnnaT620]

In the Getting Ahead Game for In/Out Grouping Games (pg. 339) - what does the In/Out Logic Chain look like? I'm stumped on how to diagram "Either Orion or Nimbler is sold at auction, but not both"

In my diagram, it looks like a bi-conditional, with the two circles at the ends of the lines - but that can't be right?! If that is the case, then would Either A or B, but not both" always be a bi-conditional?

Apologies, if this is elsewhere - not sure if this question comes from a Practice Test!

Thanks so much!
Anna

[Laura Damone]

Hi! Every game in the LG guide should be explained later in the chapter! But to you're question, you're right! It's a bi-conditional. Either/or but not both is always bi-conditional.

Good luck!

[AnnaT620]

Hi Laura,

Many thanks, that's great. Yes, I've seen this - it's just wasn't diagrammed with the logic chain (as in the Interact video) but a rule chart - just wasn't clear on what the logic chain should look like!

Thanks!