Negate the following statements formally so that **no negation symbol remains:** Negate the following statements formally so that no negation symbol remains: 
(i)  $ \ \ \forall y \exists x (y>0 \to x \leq 0 ) \ $
(ii) $ \ \forall x \forall y \exists z(x <z \leq y ) \ $
Answer:
My approach is as follows:
(i)
The negation of the statements in (i) without negation symbol is 
$ \exists y  \ \ s.t. \ \  \forall x (x>0  \to y \leq  0) \ $ 
(ii) 
Given 
$ \forall x \forall y \ \exists z \ ( x <z  \leq y ) \  \\\sim \forall x \forall y \ \exists z \ ( x <z  \wedge z \leq y ) $ 
The negation is given as  
$ \exists x \exists y \ \ s.t. \ \ \forall z  \ ( x \geq z \wedge  z > y ) $ 
Am I true ?
Is there any help ?

Your answer to (i) is wrong. The correct negation of $A\rightarrow B$ is $A\wedge \neg B$ so in your case, it should be
$\exists y \forall x (y>0) \wedge (x>0)$
which is not equivalent to the answer you have of $\exists y \forall x (x>0 \rightarrow y\leq 0)$. Your sentence is equivalent to $\exists y \forall x ( y\leq 0)\vee(x\leq 0)$, using that $A\rightarrow B$ is equivalent to $B\vee \neg A$.
Your answer to part (ii) is correct.
(EDIT): I misread your answer to (ii), confusing the conjunction with the disjunction. I is wrong, but if you make that change, it will be correct.
