Grouping Games Forum

[rbrown0824]

Does anyone have advice/methods that are useful for working grouping games? I'm trying Manhattan's Logic Chain but it only seems to complicate things. One of my biggest problems with that method is I can't tell which things absolutely must be in/out.

[CFC1524]

I'm assuming by "grouping games" you mean a regular "in-out" grouping game? So, for example, there are 7 possible ingredients that could be used in a recipe, and the game asks you questions about different combinations of those ingredients (i.e. some ingredients are "in" and some are "out")?

Step 1: Know conditional logic backwards and forwards. You should be able to draw out a series of inter-connected condtional chains and read them as if you were reading a sentence in English (this includes contrapositives as well). The chains probably seem to "complicate things" because you aren't familiar enough with conditional logic. If you're really having trouble, I'd suggest just drawing out random diagrams and practice making inferences. Make them super big and super complicated - That way, when you get to an actual in-out logic game, you'll be able to easily read / interpret your diagram.

Step 2: Practice, practice, practice

Step 3: 7sage, if you're not already using it.

Step 4: Know conditional logic backwards and forwards.

With regard to which things absolutely must be in/out, make sure you know the following:

A ---> /B means that it is impossible to have both A and B be in the "in" group. The important inference here is that one of the two letters must be in the "out" group. Keep in mind, however, that it is still possible to have both letters "out."

/A ---> B means that it is impossible to have both A and B be in the "out" group. In this case, the important inference here is that one of the two letters must be in the "in" group. Again, keep in mind that it is still possible to have both letters "in."

[rbrown0824]

Thanks for the reply! This is exactly the type of grouping game that I'm referring to. I think that I'm pretty solid on my conditional logic. The problems that I was finding with the logic chain were: 1) the diagram tended to get overly complicated/messy 2) I was unable to draw some inferences as quickly as I could with simply writing out the sentences - for example, with the statement if not a then b, I immediately knew that either a or b must be present. With the logic chain I was unable to quickly deduce this just by glancing at the diagram.

[jaysan150]

A ---> /B means that it is impossible to have both A and B be in the "in" group. The important inference here is that one of the two letters must be in the "out" group. Keep in mind, however, that it is still possible to have both letters "out."

/A ---> B means that it is impossible to have both A and B be in the "out" group. In this case, the important inference here is that one of the two letters must be in the "in" group. Again, keep in mind that it is still possible to have both letters "in."

Can you give another example using actual statements ? I am at the cusp of understanding this

[Gray]

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[rbrown0824]

For instance: If Charles is selected for the dinner then Bria is not selected- this statement is translated if C then ~B; the contrapositive is if B then ~C. If we combine these two statements we can infer that B and C will never both be selected because choosing one automatically kicks the other out. However, since our diagram only triggers a reaction when an item is known to be included, we cannot make inferences about what will happen if it is left out. Therefore, it is entirely possible that they both are out. It would be a mistake to say if ~C then ~B or vice versa. Becoming familar with this type of expression is useful for games because when you see: if X then ~Y, you can automatically say not both - only one of them will be in, or else they both will be out.

Statements such as: If Martha isn't at the dance, then Paul is there, or as we see more commonly on the LSAT: Martha goes to the dance unless Paul goes, can both can be diagrammed as ~M then P and the contrapositive ~P then M. Combining these two statements we see that leaving one of these people out will automatically force the other person in, therefore, AT LEAST one must be in at all times; they cannot both be out. The emphasis is on AT LEAST, because our diagram does not tell us what happens when either P or M is in. Therefore, we cannot make an inference there. The possibility still exists that they are both in. When you see a rule that fits the formula ~X then Y you can immediately infer that one of the two must be included and both could possible be there. Does that make sense?

[sunsheyen]

I hated the Manhattan logic chain. All those arrows and lines were too much like a terrible maze for me. Have you checked out some of J.Y.'s explanation videos on 7sage? He does it in a way that's easier to grasp, IMO.

For example, if you have:
A -> -B
if a is in, b is out, then at least one of them will always be out based on contra B -> -A, however both of them can be out as well.

-C -> B

If c is out, b is in, therefore one will always be in, contra -B -> C, but both can be in as well.

By connecting the contra of rule 2 with rule 1, you can make an easier to follow chain.

A -> -B -> C
Which lets you see that any time A is in, C is also in. The chains can continue and attach based on other rules (or their contra positives), to give a clearer picture. Much easier for me to see before I internalize the rules, than those arrows and the risk of writing them the wrong direction or losing sight of where the lines cross etc.

HTH and is even what you were talking about.

[rbrown0824]

Yes, this is absolutely what I meant. Thank you so much! Those lines were a horrible maze

[jaysan150]

I hated the Manhattan logic chain. All those arrows and lines were too much like a terrible maze for me. Have you checked out some of J.Y.'s explanation videos on 7sage? He does it in a way that's easier to grasp, IMO.

For example, if you have:
A -> -B
if a is in, b is out, then at least one of them will always be out based on contra B -> -A, however both of them can be out as well.

-C -> B

If c is out, b is in, therefore one will always be in, contra -B -> C, but both can be in as well.

By connecting the contra of rule 2 with rule 1, you can make an easier to follow chain.

A -> -B -> C
Which lets you see that any time A is in, C is also in. The chains can continue and attach based on other rules (or their contra positives), to give a clearer picture. Much easier for me to see before I internalize the rules, than those arrows and the risk of writing them the wrong direction or losing sight of where the lines cross etc.

HTH and is even what you were talking about.

Could you put parentheses and identify which part is sufficient and which part is necessary ?

[sunsheyen]

I hated the Manhattan logic chain. All those arrows and lines were too much like a terrible maze for me. Have you checked out some of J.Y.'s explanation videos on 7sage? He does it in a way that's easier to grasp, IMO.

For example, if you have:
A -> -B
if a is in, b is out, then at least one of them will always be out based on contra B -> -A, however both of them can be out as well.

-C -> B

If c is out, b is in, therefore one will always be in, contra -B -> C, but both can be in as well.

By connecting the contra of rule 2 with rule 1, you can make an easier to follow chain.

A -> -B -> C
Which lets you see that any time A is in, C is also in. The chains can continue and attach based on other rules (or their contra positives), to give a clearer picture. Much easier for me to see before I internalize the rules, than those arrows and the risk of writing them the wrong direction or losing sight of where the lines cross etc.

HTH and is even what you were talking about.

Could you put parentheses and identify which part is sufficient and which part is necessary ?

My mind doesn't really process sufficient and necessary. If I try to label in that way I get confused. I just think of if/then with if being on the left (sufficient) and then being on the right (necessary).

If the right is satisfied, then anything goes with the left (suff/ if portion of stmt) and its placement.
So in (A -> -B), if A is in, then B is out. If the necessary is satisfied, namely B being out, then the A can do anything--while conforming to any other rules affecting it. So A can be in OR out at that point because you have satisfied the rule that at least one of them is always out with B. Same applies to the contrapositive. (B -> -A) If A is out, satisfying the necessary, then B can go anywhere, because again, at least one of them is already out.

As a basic example: if I am wearing a shirt, then I can't wear a vest. So if the necessary (then/right side) is satisfied--that I'm not wearing a vest, I can wear a shirt or not, makes no difference. Sufficient can do whatever since necessary (not wearing the vest) is taken care of.
Contrapositive, if I'm wearing a vest, then I can't wear a shirt. If I'm not wearing a shirt, I can wear a vest or not, no rules are being broken.
(B -> -A) sufficient -> necessary


If the left (sufficient) isn't satisfied, then the rule is thrown out and anything goes for the variable on the right (necessary/then portion).

So with the (-C -> B), -C is sufficient (if) and B is necessary. If C is in (sufficient/if portion is failed), then the rule doesn't apply and B can do whatever. Same with the contrapositive. (-B -> C) If B is in, then it doesn't matter what C does.

Back to the example. If I'm not wearing a hat, then I will wear a vest. If the sufficient is failed, then the rule is out. So if I wear a hat, failing the sufficient, the rule doesn't matter and the vest can be on or off.

Contra is (-B -> C) is when I'm not wearing a vest, I'll wear a hat. So if the vest is on (suff failed), then the hat is free to be on or not.

For the combined rule using #1 and the contra of #2, then (A -> -B -> C) : if I'm wearing a shirt, then I'm not wearing a vest, and if not wearing a vest, I'm wearing a hat. Therefore, if I'm wearing a shirt, then I'm wearing a hat.

You can break them down into separate chunks where B is necessary in the A/B portion and sufficient in the B/C portion to work backwards in your rules. (Sufficient -> -necessary/sufficient -> necessary)

Hope that's not too crazy, doing this on my phone so I'll check its clarity later on the laptop.

[CardozoLaw09]

http://lsatblog.blogspot.ca/2009/12/log ... orest.html