~S――~W

　　~S

　　Therefore， ~W

　　This diagram shows that the argument has a valid if-then structure. A conditional statement is presented， ~S―― its premise affirmed， ~S; and then the conclusion that necessarily follows， ~W， is stated.

　　Embedded If-Then Statements

　　Usually， arguments involve an if-then statement. Unfortunately， the if-then　thought is often embedded in other equivalent structures. In this section， we study how to spot these structures.

　　Example：

　　John and Ken cannot both go to the party.

　　At first glance， this sentence does not appear to contain an if-then statement. But it essentially says： if John goes to the party， then Ken does not.

　　Example：

　　Danielle will be accepted to graduate school only if she does well on the GRE.

　　Given this statement， we know that if Danielle is accepted to graduate school， then she must have done well on the GRE. Note： Students often wrongly interpret this statement to mean：

　　If Danielle does well on the GRE， then she will be accepted to graduate school.

　　There is no such guarantee. The only guarantee is that if she does not do well on the GRE， then she will not be accepted to graduate school.

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