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Game-Like Arguments

Although they do not occur frequently, game-like arguments are common enough to warrant study.

Example: (Game)

Example
No one will be admitted to Yale Business School unless he or she studies hard for the GMAT. No one studied hard for the GMAT 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 Business School.
  2. Some graduates of Tri-State University were admitted to Yale Business School.
  3. All graduates of Tri-State University studied hard for the GMAT.
  4. Only graduates of Tri-State University did well on the GMAT.
  5. Only college graduates did well on the GMAT.
Solution
We begin by symbolizing the statements. “No one will be admitted to Yale Business School unless he or she studies hard for the GMAT” can be symbolized as
 
~SH—>~Y
 
where SH stands for “he or she studies hard for the GMAT,” and Y stands for “admitted to Yale Business 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 GMAT 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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