Tricky Logical Problem: Solving for \forallx\forally\existsz

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The logical statement \forall x \forall y \exists z (x < z \rightarrow x ≥ y) is confirmed to be true in discrete mathematics. The reasoning is that if z is chosen to be less than or equal to x, then the condition (x < z) becomes false, making the implication true regardless of the truth value of A. This understanding clarifies the logic behind the statement, demonstrating that the choice of z is crucial for validating the implication. The discussion highlights the importance of understanding implications in logical statements. Overall, the problem emphasizes the nuances of logical reasoning in mathematics.
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Homework Statement


This is a problem I have been had some troubles understanding in my Discrete Mathematics course.

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


\forallx\forally\existsz(x<z\rightarrowx≥y)



Homework Equations



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



The Attempt at a Solution



Does anyone have any ideas?
 

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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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