A
Therefore， B
This diagram displays the if-then statement “A——>B，” the affirmed premise “A
，“ and the necessary conclusion ”B.“ Such a diagram can be very helpful in s
howing the logical structure of an argument.
Example： （If-then）
If Jane does not study for the GMAT， then she will not score well. Jane， in
fact， did not study for the GMAT； therefore she scored poorly on the test.
When symbolizing games， we let a letter stand for an element. When symbolizi
ng arguments， however， we may let a letter stand for an element， a phrase， a
clause， or even an entire sentence. The clause “Jane does not study for the
GMAT“ can be symbolized as ~S， and the clause ”she will not score well“ can
be symbolized as ~W. Substituting these symbolssintosthe argument yields th
e following diagram：
~S——>~W
~S
Therefore， ~W
This diagram shows that the argument has a valid if-then structure. A condit
ional statement is presented， ~S——>~W； its premise affirmed， ~S； and then th
e 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， w
e study how to spot these structures.
Example： （Embedded If-then）
John and Ken cannot both go to the party.
At first glance， this sentence does not appear to contain an if-then stateme
nt. But it essentially says： “if John goes to the party， then Ken does not.”
Example： （Embedded If-then）
Danielle will be accepted to graduate school only if she does well on the GR
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