Confusing Bi-Conditional vs. Not Both in LG

kshutes13

Hi all,

I saw a 7sager already posted a similar question (see https://7sage.com/discussion/#/discussion/13716), but I'm less confused about what happens, and more so how we made the decision in the first place.

I was doing a problem set in which one of the rules was "F is not included in the same group as N."

At first, I drew it out as F ----> /N, which is a "not both" rule. However, when given a new premise (/F), it failed the sufficient and I didn't know what to do anymore/couldn't go any further.

Going back to JY's video explanation, I saw that he drew it out as a bi-conditional F <----> /N. When given /F, then we can conclude N is in. And then the answer is very clear.

My question is, how are we supposed to know when to use a bi-conditional and when to use a not both rule? What triggers the use of a bi-conditional? The rule "F is not included in the same group as N" spoke to me as a "not both" rule, but could also speak as a bi-conditional [(either) or but not both].

BinghamtonDave

Is the rule you referenced on a game about appetizers and main dish recipes? Is the N "Nutmeg?" I think this might hold one of the keys to understanding the subtlety here.

kshutes13

@BinghamtonDave said:
Is the rule you referenced on a game about appetizers and main dish recipes? Is the N "Nutmeg?" I think this might hold one of the keys to understanding the subtlety here.

Yes! P24 Section 4 Game 1.

bobjon1293

Edit: Misunderstood the original question.

goingfor99th

No idea if this helps:
https://i.imgur.com/bG5ExP0.jpg

Any questions, I can answer them once I have the game in front of me.

10000019

@kshutes13 said:

@BinghamtonDave said:
Is the rule you referenced on a game about appetizers and main dish recipes? Is the N "Nutmeg?" I think this might hold one of the keys to understanding the subtlety here.

Yes! P24 Section 4 Game 1.

The problem is that you treated it as an in/out, but then incorrectly captured the rule.
If you're going to treat it as an in/out, then what that rule says is
Not both (F,N) in and Not Both (F,N) out. You can then express that with a bi conditional. Alternately, you can just draw them together and put a slash on that box. That should make it clear to you that they don't go together (whether they're in or out).

Formally what this rule says:
(F or N) and not (F and N) which reduces to F xor N

kshutes13

@10000019 said:
The problem is that you treated it as an in/out, but then incorrectly captured the rule.
If you're going to treat it as an in/out, then what that rule says is
Not both (F,N) in and Not Both (F,N) out. You can then express that with a bi conditional. Alternately, you can just draw them together and put a slash on that box. That should make it clear to you that they don't go together (whether they're in or out).

Formally what this rule says:
(F or N) and not (F and N) which reduces to F xor N

Hmm okay I kind of see @10000019. So, another question I have then is:

https://7sage.com/lesson/grouping-game-1-game-board-setup/

For this grouping game, one of the rules is "V cannot be added to the same class as Z" which JY wrote as a "not both" rule. V --> /Z

For the in/out game about the appetizer and main dish, the rule was "F is not included in the same recipe as N" and JY wrote it as a bi-conditional. F <--> /N

Those two rules sound very similar in their restrictions and yet have a different way of being drawn. What is the difference here that I'm missing/how am I able to obviously & quickly detect that difference? Is it just because of the fact that they are in/out vs. grouping?

10000019

@kshutes13 said:

@10000019 said:
The problem is that you treated it as an in/out, but then incorrectly captured the rule.
If you're going to treat it as an in/out, then what that rule says is
Not both (F,N) in and Not Both (F,N) out. You can then express that with a bi conditional. Alternately, you can just draw them together and put a slash on that box. That should make it clear to you that they don't go together (whether they're in or out).

Formally what this rule says:
(F or N) and not (F and N) which reduces to F xor N

Hmm okay I kind of see @10000019. So, another question I have then is:

https://7sage.com/lesson/grouping-game-1-game-board-setup/

For this grouping game, one of the rules is "V cannot be added to the same class as Z" which JY wrote as a "not both" rule. V --> /Z

For the in/out game about the appetizer and main dish, the rule was "F is not included in the same recipe as N" and JY wrote it as a bi-conditional. F <--> /N

Those two rules sound very similar in their restrictions and yet have a different way of being drawn. What is the difference here that I'm missing/how am I able to obviously & quickly detect that difference? Is it just because of the fact that they are in/out vs. grouping?

The second game you posted has 3 groups. In my attempt at explaining it, I'm ignoring all the other rules.
1. Bi-conditionals are very restrictive. Remember you can go both ways (it's basically 2 rules).
2. ""V cannot be added to the same class as Z" means that the V and Z do not go together.
3. Not Both (V,Z) is saying that for each class you examine, V and Z are not together.
4. If you were to express that as (V<-->/Z) you've changed the meaning of the rule. If Z is in class 2, when you apply the erroneous binconditonal to class 1 and class 3, both classes now expect to have V. Yes you've separated them, but now you've added an extra constraint.
5. Now this doesn't mean you couldn't express the rule with a biconditional. It just means that if you attempt to do that, you're going to make things more difficult for yourself. If you want an example on how that rule could be captured as a biconditional in this case, let me know. I've omitted it because I think it'll just add more confusion.

akistotle

• Bi-conditional (A <---> /B; "Or, but not both rule": https://7sage.com/lesson/or-but-not-both/)

J.Y. treated PT24 S4 Game 1 (https://7sage.com/lsat_explanations/lsat-24-section-4-game-1/) as an In/Out game. The appetizer is the In group; the main dish is the Out group.

The game requires every item to be in one of the groups. The rule tells us that F and G are not supposed to be in the same group. So if we represent it as Not both rule (F ---> /G), it means that F and G could both be in the Out group. (https://7sage.com/lesson/not-both-v-or-truth-tables/) But that is not ok here.

The appetizer (In group) has to have either F or G, and the main dish (Out group) has to have either G or F, so that's why it is represented as F <---> /G.

• Not both rule (A ---> /B)

PT16 S1 Game 1 (https://7sage.com/lesson/grouping-game-1-game-board-setup/) is a Grouping Game. There are more than two groups with items that are not repeatable (each student can only be in one class). We are not treating it as a In/Out group.

J.Y. represented the rule as V ---> /Z because this means that if V is in one group, Z cannot be in that group. There is no particular Out group for this game. We look at each class (group) as "In group", and we see that if V is in a group, Z has to be in other groups (and if Z is in a group, V has to be in other groups).

If we represent it as V <---> /Z, it means class 1, class 2, and class 3 all have to have either V or Z. But that can't be right because V and Z are not repeatable in this game. There are only one V and one Z.

There are times when we have Bi-conditional (A <---> /B) in Grouping games, but that is when items are repeatable, and I think J.Y. tends to use Chart game board set up for those games.

akistotle

For these games, I think you can answer all these questions even if you misrepresented the rules, but I think this understanding is crucial when it comes to more difficult Grouping games or In/Out game.

I hope @"J.Y. Ping" can clarify the difference in one of his LG videos.

J.Y. Ping

@akistotle That's right. I don't have anything to add.

akistotle

@"J.Y. Ping" said:
@akistotle That's right. I don't have anything to add.

http://womenwriteaboutcomics.com/wp-content/uploads/2017/01/Happy-Girl-gif.gif

akistotle

@kshutes13

You may have noticed, but J.Y. puts F and S in a box and puts slash on top of it for this game (PT23.S1.Game 3):
https://7sage.com/lsat_explanations/lsat-23-section-1-game-3/

I think it's because representing is as a rule is a bit confusing. When you first start reading the stimulus of PT23.S1.Game 3, you think this is an In/Out game because we are choosing six researchers from seven. And in a way it is an In/Out game. But there are two teams within the In Group (selected group). So this is actually a Grouping game with three groups (Team 1 with three people, Team 2 with three people, and the Out group with one person).

kshutes13

Thank you @akistotle @10000019 for all your wonderful help - it is much appreciated - I think I got it now!

kshutes13

@akistotle said:
• Bi-conditional (A <---> /B; "Or, but not both rule": https://7sage.com/lesson/or-but-not-both/)

J.Y. treated PT24 S4 Game 1 (https://7sage.com/lsat_explanations/lsat-24-section-4-game-1/) as an In/Out game. The appetizer is the In group; the main dish is the Out group.

The game requires every item to be in one of the groups. The rule tells us that F and G are not supposed to be in the same group. So if we represent it as Not both rule (F ---> /G), it means that F and G could both be in the Out group. (https://7sage.com/lesson/not-both-v-or-truth-tables/) But that is not ok here.

The appetizer (In group) has to have either F or G, and the main dish (Out group) has to have either G or F, so that's why it is represented as F <---> /G.

• Not both rule (A ---> /B)

PT16 S1 Game 1 (https://7sage.com/lesson/grouping-game-1-game-board-setup/) is a Grouping Game. There are more than two groups with items that are not repeatable (each student can only be in one class). We are not treating it as a In/Out group.

J.Y. represented the rule as V ---> /Z because this means that if V is in one group, Z cannot be in that group. There is no particular Out group for this game. We look at each class (group) as "In group", and we see that if V is in a group, Z has to be in other groups (and if Z is in a group, V has to be in other groups).

If we represent it as V <---> /Z, it means class 1, class 2, and class 3 all have to have either V or Z. But that can't be right because V and Z are not repeatable in this game. There are only one V and one Z.

There are times when we have Bi-conditional (A <---> /B) in Grouping games, but that is when items are repeatable, and I think J.Y. tends to use Chart game board set up for those games.

This was an awesome explanation - thank you so much, completely cleared everything up for me. You are the best!

akistotle

@kshutes13 said:

@akistotle said:
• Bi-conditional (A <---> /B; "Or, but not both rule": https://7sage.com/lesson/or-but-not-both/)

J.Y. treated PT24 S4 Game 1 (https://7sage.com/lsat_explanations/lsat-24-section-4-game-1/) as an In/Out game. The appetizer is the In group; the main dish is the Out group.

The game requires every item to be in one of the groups. The rule tells us that F and G are not supposed to be in the same group. So if we represent it as Not both rule (F ---> /G), it means that F and G could both be in the Out group. (https://7sage.com/lesson/not-both-v-or-truth-tables/) But that is not ok here.

The appetizer (In group) has to have either F or G, and the main dish (Out group) has to have either G or F, so that's why it is represented as F <---> /G.

• Not both rule (A ---> /B)

PT16 S1 Game 1 (https://7sage.com/lesson/grouping-game-1-game-board-setup/) is a Grouping Game. There are more than two groups with items that are not repeatable (each student can only be in one class). We are not treating it as a In/Out group.

J.Y. represented the rule as V ---> /Z because this means that if V is in one group, Z cannot be in that group. There is no particular Out group for this game. We look at each class (group) as "In group", and we see that if V is in a group, Z has to be in other groups (and if Z is in a group, V has to be in other groups).

If we represent it as V <---> /Z, it means class 1, class 2, and class 3 all have to have either V or Z. But that can't be right because V and Z are not repeatable in this game. There are only one V and one Z.

There are times when we have Bi-conditional (A <---> /B) in Grouping games, but that is when items are repeatable, and I think J.Y. tends to use Chart game board set up for those games.

This was an awesome explanation - thank you so much, completely cleared everything up for me. You are the best!

Great! It might be confusing at first, but once you get it, you'll realize J.Y.'s explanations (methods) are the best for doing LG. I've done PowerScore, The LSAT Trainer....and finally got to 7Sage and went:
https://media1.tenor.com/images/b602ea45059158a615ece217544197d8/tenor.gif

hihihi9993

@akistotle said:
• Bi-conditional (A <---> /B; "Or, but not both rule": https://7sage.com/lesson/or-but-not-both/)

J.Y. treated PT24 S4 Game 1 (https://7sage.com/lsat_explanations/lsat-24-section-4-game-1/) as an In/Out game. The appetizer is the In group; the main dish is the Out group.

The game requires every item to be in one of the groups. The rule tells us that F and G are not supposed to be in the same group. So if we represent it as Not both rule (F ---> /G), it means that F and G could both be in the Out group. (https://7sage.com/lesson/not-both-v-or-truth-tables/) But that is not ok here.

The appetizer (In group) has to have either F or G, and the main dish (Out group) has to have either G or F, so that's why it is represented as F <---> /G.

• Not both rule (A ---> /B)

PT16 S1 Game 1 (https://7sage.com/lesson/grouping-game-1-game-board-setup/) is a Grouping Game. There are more than two groups with items that are not repeatable (each student can only be in one class). We are not treating it as a In/Out group.

J.Y. represented the rule as V ---> /Z because this means that if V is in one group, Z cannot be in that group. There is no particular Out group for this game. We look at each class (group) as "In group", and we see that if V is in a group, Z has to be in other groups (and if Z is in a group, V has to be in other groups).

If we represent it as V <---> /Z, it means class 1, class 2, and class 3 all have to have either V or Z. But that can't be right because V and Z are not repeatable in this game. There are only one V and one Z.

There are times when we have Bi-conditional (A <---> /B) in Grouping games, but that is when items are repeatable, and I think J.Y. tends to use Chart game board set up for those games.

Do you mind sharing an example game that shows the following incident:

There are times when we have Bi-conditional (A <---> /B) in Grouping games, but that is when items are repeatable, and I think J.Y. tends to use Chart game board set up for those games.

Thank you always @akistotle

akistotle

@d931n027h said:

@akistotle said:
• Bi-conditional (A <---> /B; "Or, but not both rule": https://7sage.com/lesson/or-but-not-both/)

J.Y. treated PT24 S4 Game 1 (https://7sage.com/lsat_explanations/lsat-24-section-4-game-1/) as an In/Out game. The appetizer is the In group; the main dish is the Out group.

The game requires every item to be in one of the groups. The rule tells us that F and G are not supposed to be in the same group. So if we represent it as Not both rule (F ---> /G), it means that F and G could both be in the Out group. (https://7sage.com/lesson/not-both-v-or-truth-tables/) But that is not ok here.

The appetizer (In group) has to have either F or G, and the main dish (Out group) has to have either G or F, so that's why it is represented as F <---> /G.

• Not both rule (A ---> /B)

PT16 S1 Game 1 (https://7sage.com/lesson/grouping-game-1-game-board-setup/) is a Grouping Game. There are more than two groups with items that are not repeatable (each student can only be in one class). We are not treating it as a In/Out group.

J.Y. represented the rule as V ---> /Z because this means that if V is in one group, Z cannot be in that group. There is no particular Out group for this game. We look at each class (group) as "In group", and we see that if V is in a group, Z has to be in other groups (and if Z is in a group, V has to be in other groups).

If we represent it as V <---> /Z, it means class 1, class 2, and class 3 all have to have either V or Z. But that can't be right because V and Z are not repeatable in this game. There are only one V and one Z.

There are times when we have Bi-conditional (A <---> /B) in Grouping games, but that is when items are repeatable, and I think J.Y. tends to use Chart game board set up for those games.

Do you mind sharing an example game that shows the following incident:

There are times when we have Bi-conditional (A <---> /B) in Grouping games, but that is when items are repeatable, and I think J.Y. tends to use Chart game board set up for those games.

Thank you always @akistotle

Hmmm I just look at a bunch of Grouping games with Chart setups, but it seems like they don't have these kind of rules. I'll post it when I find one. But what I wanted to say was that it is possible to have these rules when items are repeatable.

For example, rules like "Each group has at least A or B (but not both)" can be represented as A <---> /B

hihihi9993

@akistotle said:

@d931n027h said:

@akistotle said:
• Bi-conditional (A <---> /B; "Or, but not both rule": https://7sage.com/lesson/or-but-not-both/)

J.Y. treated PT24 S4 Game 1 (https://7sage.com/lsat_explanations/lsat-24-section-4-game-1/) as an In/Out game. The appetizer is the In group; the main dish is the Out group.

The game requires every item to be in one of the groups. The rule tells us that F and G are not supposed to be in the same group. So if we represent it as Not both rule (F ---> /G), it means that F and G could both be in the Out group. (https://7sage.com/lesson/not-both-v-or-truth-tables/) But that is not ok here.

The appetizer (In group) has to have either F or G, and the main dish (Out group) has to have either G or F, so that's why it is represented as F <---> /G.

• Not both rule (A ---> /B)

PT16 S1 Game 1 (https://7sage.com/lesson/grouping-game-1-game-board-setup/) is a Grouping Game. There are more than two groups with items that are not repeatable (each student can only be in one class). We are not treating it as a In/Out group.

J.Y. represented the rule as V ---> /Z because this means that if V is in one group, Z cannot be in that group. There is no particular Out group for this game. We look at each class (group) as "In group", and we see that if V is in a group, Z has to be in other groups (and if Z is in a group, V has to be in other groups).

If we represent it as V <---> /Z, it means class 1, class 2, and class 3 all have to have either V or Z. But that can't be right because V and Z are not repeatable in this game. There are only one V and one Z.

There are times when we have Bi-conditional (A <---> /B) in Grouping games, but that is when items are repeatable, and I think J.Y. tends to use Chart game board set up for those games.

Do you mind sharing an example game that shows the following incident:

There are times when we have Bi-conditional (A <---> /B) in Grouping games, but that is when items are repeatable, and I think J.Y. tends to use Chart game board set up for those games.

Thank you always @akistotle

Hmmm I just look at a bunch of Grouping games with Chart setups, but it seems like they don't have these kind of rules. I'll post it when I find one. But what I wanted to say was that it is possible to have these rules when items are repeatable.

For example, rules like "Each group has at least A or B (but not both)" can be represented as A <---> /B

Got it! Thanks!!!

1234abcd-1

@kshutes13 said:

@10000019 said:
The problem is that you treated it as an in/out, but then incorrectly captured the rule.
If you're going to treat it as an in/out, then what that rule says is
Not both (F,N) in and Not Both (F,N) out. You can then express that with a bi conditional. Alternately, you can just draw them together and put a slash on that box. That should make it clear to you that they don't go together (whether they're in or out).

Formally what this rule says:
(F or N) and not (F and N) which reduces to F xor N

Hmm okay I kind of see @10000019. So, another question I have then is:

https://7sage.com/lesson/grouping-game-1-game-board-setup/

For this grouping game, one of the rules is "V cannot be added to the same class as Z" which JY wrote as a "not both" rule. V --> /Z

For the in/out game about the appetizer and main dish, the rule was "F is not included in the same recipe as N" and JY wrote it as a bi-conditional. F <--> /N

Those two rules sound very similar in their restrictions and yet have a different way of being drawn. What is the difference here that I'm missing/how am I able to obviously & quickly detect that difference? Is it just because of the fact that they are in/out vs. grouping?

I have been struggling with the same thing! Okay, so I've read through the explanations below, but it's still not really making sense for me. So, is it just because of the fact that there are in/out games vs. grouping?????