Q:

Write down the negations of following statement of $∀x(x^2≥x)$

Write down the negations of following statement
$∀x(x^2≥x)$

A:

The negation of the statement above is:
$\exists x(x^2<x)~ \vee ~ \forall x(x^2\neq 2)$ 
Note that $\neg\forall \to \exists$ and vice versa $\neg\exists\to\forall$. Also $\neg\wedge\to\vee$

