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How to Use Conditional Reasoning to Crush LSAT Logic Games

Posted by Robert Fojo on Wed, Nov 12, 2014 @ 10:27 AM

logic games

The LSAT Logic Games section is the shortest section of the LSAT.  Yet it often provokes the strongest feelings among LSAT test-takers.  People either love this section, or they hate it.

Both sides have a point.  LSAT Logic Games either confuse or stimulate curiosity.  The key to doing well on, and mastering, these Games is paying careful attention to detail.  Pay very careful attention to the information these Games present, and extract as much additional data from that information as possible.

One area where this skill can be applied is in conditional reasoning.  The LSAT Logic Games section often uses conditional reasoning (e.g., If A, then B) to express one or more rules, ask questions, and, in the process, confuse students.  The key to overcoming the LSAT’s use of conditional reasoning is to understand critical differences between conditional statements and then to use these statements to draw helpful inferences. 

What is Conditional Reasoning?

Conditional reasoning is an area of logic that is prevalent mostly on the Logical Reasoning and Logic Games sections of the LSAT.  It involves the use of “sufficient” and “necessary” conditions.  Students should have a firm grasp of these concepts in general to perform well on the LSAT.

A “sufficient” condition literally refers to something that is “enough.”  It implies the existence of something else.  On the LSAT, it will usually take the form of the statement “If A is in Group 1, then B is in Group 1.”  That means that the condition “A is in Group 1” is sufficient for B to be in Group 1.

In contrast, a “necessary” condition literally refers to something that is “required.”  Unlike a sufficient condition, it does not yield an inference.  Thus, the condition above that “B is in Group 1” does not mean that A is also in Group 1.  It simply means that it is possible A could be in Group 1.

How the LSAT Uses Conditional Reasoning to Confuse Students

The LSAT will attempt to make students confuse something that is required for an event to occur for something that is sufficient for an event to occur, and vice versa. 

Let’s consider the following hypothetical example on an LSAT Logic Game:

If Braden is placed in English 102, then Celeste is not placed in English 102.

This is a common rule that appears on a Logic Game that involves pure grouping where certain variables are either “in or out” of a certain arrangement.  This particular Game will usually entail some grouping of students in a class, and the rules that are provided will require you to plug in certain students in that class and exclude others.  The rule above tells us that, if Braden is placed in English 102, that event implies that Celeste will not be placed in English 102.  We would diagram this rule as follows:

                  B --> C

The contrapositive of this rule would be, “If Celeste is placed in English 102, then Braden is not placed in English 102.”  We would diagram the contrapositive as follows:

                  C --> B

Now consider if one of the rules or questions in this Logic Game presented you with the following slightly different statement:

If Braden is not placed in English 102, then Celeste must be placed in English 102. 

This is a slightly different statement, but it has major implications when it is applied.  In contrast to the first rule above, this second rule tells us that, if Braden is not placed in English 102, then that event implies that Celeste will have to be placed in English 102.  We would diagram this rule as follows:

                  B --> C

The contrapositive of this rule would be, “If Celeste is not placed in English 102, then Braden must be placed in English 102.”  We would diagram it as follows:

                  C --> B 

These two rules appear similar, but they apply themselves differently.  The test writers will often try to confuse you with similarities like these.  You will have to recognize the differences and diagram/document them correctly. 

How to Use Conditional Statements to Identify Scenarios

Recognizing the differences between conditional statements is one thing.  Using them to draw proper inferences is another animal altogether.  This is where you earn your money on the LSAT.

To perform well (or exceptionally well) on LSAT Logic Games, you need to infer additional rules from the rules that are provided.  Developing and applying this skill will help you answer questions more quickly.  If you are aiming for a very high score, it will, in part, mean the difference between missing a few questions on this section, and answering every question correctly.

To draw proper inferences, it helps first to identify scenarios yielded by a given rule.

Let’s do this with our first rule above:

If Braden is placed in English 102, then Celeste is not placed in English 102. 

You will recall that we diagrammed this rule as follows:

B --> C

This rule yields FOUR potential scenarios.  Your ability to recognize and document these four scenarios will determine how well you will perform on this particular Logic Game, and how quickly you can answer the questions.  The four scenarios are the following:

1)     B is placed in English 102; C is out

This scenario is a straight application of the rule above.  If B is placed in English 102, then C cannot be placed in the same class.  Otherwise, it would be a violation of the rule.

2)     C is placed in English 102; B is out

This scenario is a straight application of the contrapositive of the rule above. If C (instead of B) is placed in English 102, then B cannot be placed in the same class.  Otherwise, it would be a violation of the rule.

3)     Both B and C are placed in English 102 = Not Possible

This scenario is not possible and can never happen.  Neither the rule (Scenario 1 above) nor its contrapositive (Scenario 2 above) permit this scenario from occurring. 

4)     Neither B nor C is placed in English 102 = Possible

Although both B and C cannot be placed in English 102 (Scenario 3 above), it is possible for neither C nor C to be placed in English 102.  The rule and its contrapositive do not prohibit this scenario.  The rule applies only if either B or C is placed in English 102.  If neither is placed in English 102, then the rule does not apply.  If B was not placed in English 102, that does not mean C must automatically be placed in the class.  Instead, C also could be excluded from English 102.

Notice that these scenarios would not play out in the same way if, instead, we were dealing with a Logic Game that involved two separate groups (i.e., Team 1 or Team 2; or Group 1 or Group 2), where certain variables were either in one group or the other, as opposed to our Game above, where they are either “in or out.”  In that case, the scenario where neither B nor C is selected would not be possible.

However, here, it is possible because there is no other class (that we know of) where B or C could be placed.  Our rule deals only with the people who are placed in English 102; it does not deal with the people who are not placed in English 102.

Let’s now identify the scenarios yielded by our second rule:

                  If Braden is not placed in English 102, then Celeste must be placed in English 102.

You will recall that we diagrammed this rule as follows:

B --> C

Like our first rule, this rule yields FOUR potential scenarios:

1)     B is not placed in English 102; C is placed in English 102

This scenario is a straight application of the rule above.  If B is not placed in English 102, then C must be placed in the class.  Otherwise, it would be a violation of the rule.

2)     C is not placed in English 102; B is placed in English 102

This scenario is a straight application of the contrapositive of the rule above. If C (instead of B) is not placed in English 102, then B must be placed in the class.  Otherwise, it would be a violation of the rule.

3)     Neither B nor C is placed in English 102 = Not Possible

This scenario is the opposite of our other Scenario 3.  Whereas the former stated that placing both B and C in English 102 was not possible, this rule dictates that placing neither in English 102 is not possible.  In other words, you can never have an English 102 class where both B and C are not placed in it.

4)     Both B and C are placed in English 102 = Possible

Although both B and C cannot be excluded from English 102 (Scenario 3 above), it is possible for both C and C to be placed in English 102.  The rule and its contrapositive do not prohibit this scenario.  The rule applies only if either B or C is not placed in English 102.  If both are placed in English 102, then the rule does not apply.  If B was placed in English 102, that does not mean C must automatically be excluded from the class.  Instead, C also could be placed in English 102.

Some students will get confused with this scenario and will not anticipate it.  They will conclude that either B or C must be placed in English 102, but they will not conclude that both could be placed in the class.

How to Use Conditional Statements to Draw Inferences

As noted above, to perform well on LSAT Logic Games, you must draw as many inferences as possible from the rules provided. 

With respect to our first rule above (If Braden is placed in English 102, then Celeste is not placed in English 102; or B --> C), the first set of scenarios we predicted above help us draw two inferences:

First, we can draw the inference that, at all times, at least either B or C will not be placed in English 102.  This is reflected in Scenarios 1 and 2.  When you diagram this Logic Game, you would make a note of this inference on your diagram. 

Second, we can draw the inference that there will never be a situation where both B and C are placed in English 102 (Scenario 3).  Again, you would make a note of this inference on your diagram.

Note that we cannot draw the inference that, at all times, at least either B or C will be placed in English 102.  Rather, both could be excluded, as reflected by Scenario 4 above.

With respect to our second rule above (If Braden is not placed in English 102, then Celeste must be placed in English 102; or B --> C), the second set of scenarios we predicted above also help us draw two inferences:

First, we can draw the inference that, at all times, at least either B or C will be placed in English 102.  This is reflected in Scenarios 1 and 2.  You would make a note of this inference on your diagram.

Second, we can draw the inference that there will never be a situation where neither B nor C is placed in English 102 (Scenario 3).  You would note that as well on your diagram.

Note that we cannot draw the inference that, at all times, at least either B or C will not be placed in English 102.  Rather, both could be included, as reflected by Scenario 4.

These are quick inferences you can make with this type of Logic Game.  They don’t help you know everything about the Game, but they help you learn enough to help you answer certain questions rapidly. 

Conditional reasoning can often pose difficult problems for students.  The key to overcoming these difficulties is to understand critical differences between conditional statements and then to use these statements to draw specific inferences that help you map out the possibilities in a Logic Game and then answer questions about those possibilities.

About the Author:

This article was written by Robert M. Fojo from LSAT Freedom.  Robert graduated from Harvard Law School and is a co-founder of LSAT Freedom, an online LSAT prep course that emphasizes learning the logic on the exam and then applying that knowledge through practice with real LSAT questions.  Robert frequently writes about tips and strategies for doing well on the LSAT.  To get other helpful ideas for performing well on the LSAT and improving your score, join LSAT Freedom’s free newsletter

 

 

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