MHB Is this the correct way to negate a mathematical statement?

[tmt1]

$\forall $ positive real numbers $r$ and $p$ if $p \cdot r >= 100 $ then either $r$ or $p$ is greater than $10$

I am going for

$\exists$ positive real numbers $r$ and $p$ such that if $p \cdot r >= 100 $ then both $r$ or $p$ is lesser or equal to $10$Is this right?

 

[Deveno]

Close.

You are correct that the negation of:

$\forall x,y \in S: P(x,y)$

is:

$\exists x,y \in S: \neg(P(x,y))$

but you're slightly off on the negation of an implication.

The negation of: $A \implies B$ isn't $A \implies \neg B$, but rather: $A\ \&\ \neg B$.