Is the following statement true or false??(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\forall x[x^2\leq 0\Longrightarrow x>0][/tex]

Solution No 1: since [tex]x^2\geq 0[/tex] for all ,x the above statement is "vacuously satisfied"

Solution No 2: the negation of the above statement is:

[tex]\exists x[x^2\leq 0[/tex] and [tex]x\leq 0[/tex] .But since [tex]x\leq 0\Longrightarrow x^2\geq 0[/tex].So we have : [tex]x^2\geq 0[/tex] and [tex]x^2\leq 0[/tex] ,which implies that x=0.

So there exists an element x=0.Hence the negation is true and thus the above statement is false

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# True,false statement

**Physics Forums | Science Articles, Homework Help, Discussion**