Hello Juancd08I think this is all to do with a false statement implying a statement which may be true or false. See the third and fourth lines of the Truth Table: Discrete mathematics/Logic/Page 2 - Wikibooks, collection of open-content textbooks.

when

when

So if is real, the minimum value of is , and therefore has no real solutions.

So if is the propositional function: and is the propositional function :

, since is always false

i.e. for all real values of .

Grandad