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 logic， 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 precisely 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.