Forming a negation of a statement (∀x∈A)(∀y∈B)((x=y)⇒(y>2)) I have a statement from which I need to form a negation.
$$(\forall x \in A)(\forall y \in B)((x=y)\to (y>2))$$
Could this solution be correct?
$(\exists x \in A)(\exists y \in B)((x=y)\land(y\leq 2))$
or could it be solved like this
$(\exists x \notin A)(\exists y \notin B)((x=y)\land(y\leq 2))$ or $¬(\exists x \in A)(\exists y \in B)((x=y)\land(y\leq 2))$
as well?  
Thank you.
 A: The sentence is telling: 
If any two elements $x$ living in $A$ and $y$ living in $B$ are equal, then $y$ will be greater than $2$.
The negation is:
There are two elements $x$ living in $A$ and $y$ living in $B$ that are equal and $y$ is not greater than $2$. 
That's why I think: only your first answer is correct.
We can write $$(\forall x \in A)(\forall y \in B)((x=y)\to (y>2))$$ by the rule of inference as
$$ (\forall x \in A)(\forall y \in B)(\neg(x=y)\lor (y>2))$$
Then the negation changes $$\forall x,\forall y,\neg (x=y) \lor (y>2)$$ to $$\exists x,\exists y,\neg\neg(x=y) \land (y\leq2)$$ 
and by the double negation elemenation rule $\neg\neg(x=y)\Rightarrow (x=y) $. That's why the negation is:
$$(\exists x \in A)(\exists y \in B)((x=y)\land (y \leq 2))$$ 
also have a look here
Statement $\rightarrow$    Negation
"A or B" $\rightarrow$ "not A and not B"
"A and B"   $\rightarrow$ "not A or not B"
"if A, then B" $\rightarrow$   "A and not B"
"For all x, A(x)" $\rightarrow$    "There exist x such that not A(x)"
"There exists x such that A(x)" $\rightarrow$  "For every x, not A(x)"
