Pratheep Sevanthinathan - smarTEST Prep: Guide to LSAT Logic Games

We would like to thank Shantel Miller for her illustrations throughout this manual, and to Alexis Sharp for her tireless proofreading, feedback, comments, and assistance. This book would not have been possible without your help.

Appendix A FORMAL LOGIC

Appendix B SYMBOLOGY

Deductive Reasoning is the process of using general statements or premises to reach specific conclusions. Here is an example:

All humans are mammals.

I am a human.

Therefore, I am a mammal.

If the rules of deductive logic are followed and the premises are true, then the conclusion must necessarily be true.

Thus, if you properly use deductive logic on the LSAT, and the premises are true (which will be on the LSAT) then your conclusions will also be true. [This is an example of deductive logic!]

The LSAT tests deductive reasoning. Be careful not to confuse deductive reasoning with inductive reasoning, which is the process of reasoning from specific examples to reach general conclusions. Inductive arguments can be strong or weak, but deductive arguments can be valid or invalid. The LSAT tests whether you can make valid deductive arguments.

Formal logic, in the realm of the LSAT, is a system of deductive reasoning. It is the primary concept tested in the LSAT Logic Games section. On test day, you will be presented if-then statements, such as If Alice dances first then Beth dances fourth. The statement if A is 1st, then B is always 4th is a deductive formal logic statement.

If-then statements are conditional statements. If a certain condition is met, a result will occur.

If-then statements can be presented in a variety of ways. Here are several different ways If Alice dances first then Beth dances fourth can be written:

• If Alice dances first then Beth dances fourth.
• Alice dances first only if Beth dances fourth.
• Alice dances first if, and only if, Beth dances fourth.
• Beth always dances fourth if Alice dances first.
• When Alice dances first, Beth dances fourth.
• Alice dances first only when Beth dances fourth.
• If Alice dances fourth, Beth must dance fourth.

All of the above statements are equivalent and mean the same exact thing. Notice that, although these are all considered if-then statements, they do not all contain the words if or then.

All of the above statements can be represented very easily in a diagram using a simple arrow. If Alice dances first then Beth dances fourth is represented symbolically as A B. At the back end of the arrow is the if entity, and the front end of the arrow is the then entity. A is the trigger, and B is the result. Thus, no matter how the logical statement is presented, it can be simply diagrammed as:

The contrapositive is an inverted manner to express a conditional statement. Every conditional statement has a contrapositive. A conditional statement and its contrapositive are logically equivalent, i.e. they mean the same thing.

For example, the logical statement If Alice dances first then Beth dances fourth, can also be written in these inverted contrapositive forms:

• If Beth does not dance fourth, then Alice does not dance first.
• If Beth does not dance fourth, then Alice cannot dance first.
• When Beth does not dance fourth, Alice does not dance first.

Proper use of the Contrapositive is a critical skill that will either simplify your game setup or jeopardize the entire diagram. If a logical rule is true, then its contrapositive must also be true.

We can demonstrate this by using a contrapositive example from real life. Consider the following rule:

If the sun is visible in the sky, then it must be daytime.

S D

In order to get the contrapositive, negate both statementsandflip the arrow:

Not D not S

If it is not daytime, the sun is not visible in the sky.

But proceed with Caution: DO NOT negate the statements without flipping the arrow and DO NOT flip the arrow without negating the statements!!! If you make an improper negative deduction, the result would be:

Not D not S

If the sun is not visible, then it cannot be daytime.

Our real life example demonstrates the limits of a proper contrapositive. If the sun is visible in the sky, it must be daytime. If it is not daytime, then the sun is not visible in the sky.

However, just because the sun is not visible in the sky does not necessarily mean that it is not daytime. The sun could be obstructed by fog, or covered by clouds and rain. It is entirely possible for it to be daytime but for the sun to not be visible.

Use contrapositives properly and wisely to make deductions!

Using uniform symbols to represent logic is key to success in the Logic Games section. There are many different ways in which you can visually represent logic that is provided on the LSAT, and there is no correct way to symbolize the logic. We recommend using the symbols below, as they will allow you to maintain consistency throughout.

Symbol	Translation	Usage	Ordering	Non-Ordering
Arrow A B	If-Then	Represents an if-then or trigger-result relationship. The arrow can go either any direction, with the if or trigger on the back end of the arrow, and then then or result going on the front end of the arrow.	If Al shoots first, then Bud shoots fourth: A B	If Al drinks wine, then Bud also drinks wine: Wine Beer H20 A B
Circled Entity	Always goes in designated spot.	Represents a must be true or always true logical statement.	One of the girls finishes third:	Bud drinks wine:
Multiple Circled Entities	Ordering : Entities are consecutive, as drawn. Non-Ordering : Entities always go together.	Ordering : Represents the relationship that two entities must be consecutive, as drawn. If the entities are consecutive but not in a specific order, then a double arrow must be placed above to indicate this.