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Game-Like Arguments

Although they do not occur frequently, game-like arguments are common enough to warrant study.  Game-like arguments are symbolized just like logical structure arguments, but in these cases you will be asked to draw a conclusion.

Example: (Game)

Example
No one will be admitted to Yale Law School unless he or she studies hard for the LSAT.  No one studied hard for the LSAT unless he or she was not a graduate from Tri-State University.
 
Which one of the following conclusions necessarily follows from the above statements?
  1. No graduate of Tri-State University was admitted to Yale Law School.
  2. Some graduates of Tri-State University were admitted to Yale Law School.
  3. All graduates of Tri-State University studied hard for the LSAT.
  4. Only graduates of Tri-State University did well on the LSAT.
  5. Only college graduates did well on the LSAT.
Solution
We begin by symbolizing the statements.  “No one will be admitted to Yale Law School unless he or she studies hard for the LSAT” can be symbolized as
 
~SH—>~Y
 
where SH stands for “he or she studies hard for the LSAT,” and Y stands for “admitted to Yale Law School.”
 
The second condition appears confusing at first but is actually straightforward once we get around the obfuscating tactics. “No one studied hard for the LSAT unless he or she was not a graduate from Tri-State University” can be symbolized as
 
~(~G)—>~SH
 
where G indicates “a graduate of Tri-State University.” Recalling that two negatives make a positive, we simplify this to
 
G—>~SH
 
Using the transitive property to combine this with the first premise, ~SH—>~Y, yields
G—>~Y
 
In other words, if a person graduated from Tri-State University, he or she was not admitted to Yale. The answer is (A).
 





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