LSAT Logic Games: Intro To In/Out Grouping Games

Learn about In/Out Grouping Games on the LSAT with this excerpt from THE BRIEF, Manhattan Prep’s free LSAT prep email series.

Ed. note: The below “LSAT Logic Games: In/Out Grouping Games” content is an edited excerpt from THE BRIEF, the new LSAT prep  email series created by a team of 99th percentile LSAT instructors at Manhattan Prep. THE BRIEF is ideal for anyone looking for a structured, comprehensive way to prep for the LSAT on their own. And it’s free to use. Just select your frequency, sign up, and start making progress toward your law school dream.

In/Out Grouping games are a standard type of logic game seen on the LSAT. They’re not as common as other types of games, and you definitely aren’t guaranteed to see one on your test. However, they’re still frequent enough that you’ll want to be prepared in case one shows up, and they also provide a good opportunity to strengthen your conditional logic skills.

We’ve created both text and video tutorials so that you can choose the delivery mode that helps you learn best. Feel free to mix and match them as you see fit.

In/Out Grouping Games: Two By Two, Side By Side

An In/Out Grouping game will have two identifying characteristics: the game will assign elements to one of two groups (almost always an “In” group and an “Out” group), and most or all of the rules will contain conditional statements. Since conditional logic plays an important role in In/Out Grouping, be sure to review that content while learning this material.

The scenario of an In/Out Grouping game often describes elements that are being selected for something. For example, there might be five players — Q, R, S, T, and U — trying out for a professional knitting team. Some will be selected for the team, and some won’t. We might label the two groups “Selected” and “Unselected,” but we usually just call them “In” and “Out.”

While almost all In/Out Grouping games will be similar to this one in that they split elements between being selected and unselected for a “team,” there’s another possibility: two teams. Maybe the game asks you to split players between the Purple Parrots and the Silver Monkeys. Maybe it asks you to figure out who’s a doctor and who’s a lawyer. Or maybe it asks you to determine whether the dress is a part of the fall line or the spring line. Whatever the case, the binary scenario (i.e., having two groups) is the important facet.

The Logic Chain

Like the Relative Ordering Tree, the diagram for this game type (the Logic Chain) is not intuitive. However, it’s powerful and will make inferences for us. So strap in for a bumpy ride, because this isn’t easy to learn, but it’s super powerful once you understand it.

Some or all of the rules for an In/Out Grouping game will be conditional rules that describe which elements go together in a group and which go in different groups. Here are some examples, based on our knitting team tryouts:

If Q is selected then R is selected.

If S is not selected then U is selected.

If R is selected then S is not selected.

The Logic Chain is a diagram that lets us represent the rules and see how they are connected. To create a Logic Chain, start with two columns. We’ll call these the “In” and “Out” columns to describe who is selected for the team, and who isn’t.

Once we’ve labeled our columns, we’ll start adding our elements. However, don’t just list them out (we’ll see why in a minute). The first rule above involves Q and R, so we’ll place each of these elements on the diagram twice, once in each column, about halfway down (again, bear with us). Next, we’ll use arrows to represent the conditional rules.

The first rule tells us that if Q is selected, R is also selected, or Q → R. To place this on the Logic Chain, we draw an arrow from Q in the “In” column to R in the “In” column.

We also diagram the contrapositive of this rule: Not R → Not Q. This gives us an arrow from R in the Out column to Q in the Out column.

Similar to what you would do in a Relative Ordering Tree, you should jump to rules that overlap with the elements already in the Logic Chain. The second rule doesn’t share any elements with the first rule, so let’s skip it for now. The third rule also talks about R, though, so let’s get it into our diagram.

To diagram the third rule — If R is selected then S is not selected — we add an S to both columns below the R, then draw an arrow crossing from R in the In column to S in the Out column. The arrow from S in the In column to R in the Out column represents the contrapositive. This rule also lets us see why we didn’t just list out the elements — we want to keep elements that are linked together by the rules close to each other so our diagram is easy to follow!

Now that S is in the Logic Chain, we can incorporate the second rule. Place a U below S in both columns, and connect the elements to represent the rule:

Again, note that building the Logic Chain by taking the rules out of order, based on shared elements, creates a much cleaner look than if you simply listed all elements in both columns up front!

So what does this get us? There are three main benefits to the Logic Chain:

  1. Contrapositives: Taking the contrapositive is quick and easy (well, easier). You can do it visually. To take the contrapositive of a rule that crosses the columns, the contrapositive crosses the arrows. To take the contrapositive of a rule that stays in the same column, the contrapositive finishes a box between those elements. Check above to see how that works!
  2. Connecting inferences: Second, third, and even later-step connecting inferences are made for you by the Chain! If you start anywhere, you can follow the arrows to make inferences. As an example, if a Conditional question states that U is out, starting with U out and following the arrows tells us S is in, R is out, and Q is in! Those inferences involve all 3 rules, but require no additional work once you’ve built your chain.
    1. Remember: Arrows go in only one direction. Don’t go against the grain when making inferences! If R is out, you can infer that Q is also out, but you can’t go against the arrow to infer that S is in.
  3. Advanced inference visualization: Certain types of advanced inferences are much easier to visualize with the Logic Chain than with the conditional statements just written out.

These benefits are what make the Logic Chain so great. (No, really. It’s like that weird show that you didn’t like at first, but that you watch all the time now. Give it time!)

Every Which Way but Logic

Suppose this game has two more rules:

If Q is selected then T is not.

If T is not selected then Q is.

These two rules give us a biconditional. For the first rule, we need an arrow from Q in the In column to T in the Out column. The contrapositive gives us an arrow from T in the In column to Q in the Out column. This is similar to our previous rule about R and S.

The second rule gives us an arrow from T in the Out column to Q in the In column. For the contrapositive, we have an arrow from Q in the Out column to T in the In column.

The end result is a double-headed arrow going between Q in In and T in Out, and another double-headed arrow between T In and Q Out. We can follow these lines in either direction. Since we normally aren’t allowed to read backwards against an arrow, it’s helpful to use dots instead of arrows on the ends of these lines. That just reminds us that these are biconditionals.

Biconditionals are very important in Logic Games, and in In/Out Games in particular. They’re some of the strongest rules out there, and they provide an option (here, either T is in with Q out, or Q is out with T in). If the biconditional is connected to other rules, it might be beneficial to build frames around the two possible orientations.

There are three primary ways the LSAT will introduce a biconditional:

  1. As stated here: a conditional rule and the reverse (or negation) of that rule will both be given.
  2. An if and only if statement (e.g., Q is selected if and only if T is not).
  3. An at least one, but not both statement (e.g., Either Q is selected, or T is selected, but not both).

Is There Anything It Can’t Do?

Sadly, yes. There are two ways the Logic Chain can go off the rails (though neither are common):

  1. Non-splittable complex conditionals (i.e., conditionals with “and” or “or”): If you can’t split your conditional statement because of the location of the “and” or “or” statements, you can’t get them into your chain. If there’s just one of them, write it off to the side and throw an asterisk in the chain next to the sufficient conditions. If there are more than one, fall back on writing out the conditional statements individually.
    1. Can’t be split (will break the chain): “and” in the sufficient condition; “or” in the necessary condition
    2. Can be split (work with the chain): “or” in the sufficient condition; “and” in the necessary condition
  2. All of the conditionals “point” in the same direction (e.g., they all point from the “In” column to the “Out” column, or vice versa): In this case, the rules won’t chain together, so you need to fall back on listing the conditionals. In this case, however, pay attention to the element(s) in the most rules, and the element(s) in the least rules. They’re generally the ones that show up in each correct answer.

In spite of its limitations, the Logic Chain can be a powerful tool for conquering In/Out Grouping games. As a teaser, see if you can figure out what this next diagram means:

                                                                                                                               

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