Question

D. Let P(x) denote the statement 𝟏 𝒙 𝟐+𝟏 > 1. If its domain are all real numbers, what is the truth value of the following quantified statement? (5 pts each) 1. ∃xP(x) 2. ∀xP(x)

Answer 1

$x^2+1>1\Leftrightarrow x\ne 0\\1:\\\exists xP\left( x \right) =True: for\,\,x=1 holds\\2:\\\forall xP\left( x \right) =False: for\,\,x=0 does\,\,not\,\,hold$