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Tricky Logical Problem

  1. Sep 24, 2013 #1
    1. The problem statement, all variables and given/known data
    This is a problem I have been had some troubles understanding in my Discrete Mathematics course.

    [PLAIN]http://i.imgur.com/HTUNr7f.png[/PLAIN]


    [itex]\forall[/itex]x[itex]\forall[/itex]y[itex]\exists[/itex]z(x<z[itex]\rightarrow[/itex]x≥y)



    2. Relevant equations

    I know that this statement is true, according to the solutions page, but I just cannot comprehend why?



    3. The attempt at a solution

    Does anyone have any ideas?
     

    Attached Files:

  2. jcsd
  3. Sep 30, 2013 #2
    The statement is true, because if you choose z to be less or equal to x, then (x < z) is a false statement, so (x < z ) -> A is always true, regardless of "A".
     
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