WS

　　SL

　　Therefore， WL

　　The diagram clearly displays the transitive property.

　　DeMorgans Laws

　　~ = ~A or ~B

　　~ = ~A ~B

　　If you have taken a course in logic， you are probably familiar with these formulas. Their validity is intuitively clear： The conjunction AB is false when 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 rulesthey are too mechanical. Nevertheless， DeMorgans laws often help simplify， clarify， or transform parts of an argument. They are also useful with games.

　　Example：

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

　　This argument can be diagrammed as ~， which by the second of DeMorgans laws simplifies to 。 This diagram tells us that neither of th

　　A unless B

　　~BA

　　A unless B is a rather complex structure. Though surprisingly we use it with little thought or confusion in our day-to-day speech.

　　To see that A unless B is equivalent to ~BA， consider the following situation：

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