Mệnh đề đúng hoặc sai :
$a)   \forall  x\in R, \forall  y \in R: x>y\Rightarrow \frac{1}{x}<\frac{1}{y}  $
$b)   \forall  x\in R, \forall  y \in R:x>y\Leftrightarrow  x^3>y^3$
$c)   \forall  x\in R,\forall  y \in R:x>y\Leftrightarrow  x^2>y^2$
$d)   \forall  x\in R, \forall y\in R:x>y\Rightarrow \sqrt{x}>\sqrt{y}  $
$a)$ Mệnh đề sai.
Chọn $x=2,y=-1\Rightarrow x>y$ nhưng $\frac{1}{x}=\frac{1}{2}>\frac{1}{-1}=\frac{1}{y}$
$b)$ Mệnh đề đúng, vì $x^3-y^3=\left ( x-y \right )\left ( x^2+xy+y^2 \right )=\left ( x-y \right )\left[ {\left ( x+\frac{y}{2} \right )^2+\frac{3}{4}y^2} \right]   $
$c)$ Mệnh đề sai,chọn $x=1,y=-2$.
$x>y$ nhưng $x^2=1<4=y^2.$ Suy ra vô lý.

$d)$ Mệnh đề sai,chọn $x=5,y=-1$.
$x>y$ nhưng $\nexists \sqrt y$. Suy ra vô lý.

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