One way of doing this is to notice that (a→b) is logically equivalent to (¬a ∨ b)
Then ¬(a→b) is equivalent to ¬(¬a ∨ b) which is equivalent to ¬¬a ∧ ¬b or a ∧ ¬b.
Here a is the statement that "x*y is even"; b is the statement (x is even ∨ y is even) where ∨ is or
The negation will be a ∧ ¬b or (x*y is even) ∧ ¬((x is even) ∨ (y is even))
We can simplify this expression to (x*y is even) ∧ (¬(x is even) ∧ ¬(y is even))
Which simplifies to (x*y is even) ∧ ((x is odd) ∧ (y is odd))
So one form of the negation is "The product x*y is even and x is odd and y is odd". This statement is of course FALSE because an odd*odd is always odd. We negated a statement that is always true, so it is logical that we should arrive at this conclusion.