# Tricky Logical Problem

1. Sep 24, 2013

### studas

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]

$\forall$x$\forall$y$\exists$z(x<z$\rightarrow$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?

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2. Sep 30, 2013

### csopi

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".