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

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# True,false statement

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