Let W stand for “you work hard，” S stand for “you will be successful in Amer

　　ica，“ and L stand for ”you can lead a life of leisure.“ Now the first senten

　　ce translates as W——>S， the second sentence as S——>L， and the conclusion as

　　W——>L. Combining these symbol statements yields the following diagram：

　　W——>S

　　S——>L

　　Therefore， W——>L

　　The diagram clearly displays the transitive property.

　　DeMorgan's Laws

　　~（A & B） = ~A or ~B

　　~（A or B） = ~A & ~B

　　If you have taken a course in logic¹， you are probably familiar with these fo

　　rmulas. Their validity is intuitively clear： The conjunction A&B is false wh

　　en either， or both， of its parts are false. This is precisely² what ~A or ~B

　　says. And the disjunction A or B is false only when both A and B are false，

　　which is precisely what ~A and ~B says.

　　You will rarely get an argument whose main structure is based on these rules

　　——they are too mechanical. Nevertheless， DeMorgan's laws often help simplify

　　， clarify， or transform parts of an argument. They are also useful with game

　　s.

　　Example： （DeMorgan's Law）

　　It is not the case that either Bill or Jane is going to the party.

　　This argument can be diagrammed as ~（B or J）， which by the second of DeMorga

　　n's laws simplifies to （~B and ~J）。 This diagram tells us that neither of th

　　em is going to the party

A unless B

　　~B——>A

　　“A unless B” is a rather complex structure. Though surprisingly we use it wi

　　th little thought or confusion in our day-to-day speech.

　　To see that “A unless B” is equivalent to “~B——>A，” consider the following s

　　ituation：

　　Biff is at the beach unless it is raining.

　　Given this statement， we know that if it is not raining， then Biff is at the

　　beach. Now if we symbolize³ “Biff is at the beach” as B， and “it is raining”

　　as R， then the statement can be diagrammed as ~R——>B.

　　CLASSIFICATION

　　In Logic II， we studied deductive arguments. However， the bulk of arguments

　　on the GMAT are inductive. In this section we will classify and study the ma

　　jor types of inductive arguments.

　　An argument is deductive if its conclusion necessarily follows from its prem

　　ises——otherwise it is inductive. In an inductive argument， the author presen

　　ts the premises⁴ as evidence or reasons for the conclusion. The validity of t

　　he conclusion depends on how compelling the premises are. Unlike deductive a

　　rguments， the conclusion of an inductive argument is never certain. The trut

　　h of the conclusion can range from highly likely to highly unlikely. In reas

　　onable arguments， the conclusion is likely. In fallacious arguments， it is i

　　mprobable. We will study both reasonable and fallacious arguments.

　　We will classify the three major types of inductive reasoning——generalizatio

　　n， analogy， and causal——and their associated fallacies.

　　Generalization⁵

　　Generalization and analogy， which we consider in the next section， are the m

　　ain tools by which we accumulate knowledge and analyze⁶ our world. Many peopl

　　e define generalization as “inductive reasoning.” In colloquial⁷ speech， the

　　phrase “to generalize” carries a negative connotation. To argue by generaliz

　　ation， however， is neither inherently good nor bad. The relative validity of

　　a generalization depends on both the context of the argument and the likeli

　　hood⁸ that its conclusion is true. Polling organizations make predictions by

　　generalizing information from a small sample of the population， which hopefu

　　lly represents the general population. The soundness of their predictions （a

　　rguments） depends on how representative the sample is and on its size. Clear

　　ly， the less comprehensive a conclusion is the more likely it is to be true.

　　Example

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