Answer to Question #142283 in Discrete Mathematics for Ana belle

Question

Find a counter example to the following universally quantified statements, where the domain for all variables consist of all integers. ∀x, x^2, <=x^3.

Answer 1

Let us find a counter example to the following universally quantified statement, where the domain for all variables consist of all integers:

$\forall x (x^2\leq x^3)$

Indeed, for the integer number $x=-2$ we have that $x^2=4, x^3=-8$. Therefore, it is not true that

$x^2\leq x^3$.