Help needed with converting sentence to predicate logic

Question

Say x represents real numbers and E(x) represent Even numbers and I(x) represents Integers.

How would you convert this sentence to predicate logic?
No even integers are odd

Here's my attempt, but I have a feeling it could be wrong
¬ ∀x ( E(x) ^ I(x) => ¬E(x) )

Answer 1

Your sentence $\neg \forall x ( (E(x) \land I(x)) \rightarrow \neg E(x) )$ is saying that 'not all even integers are not even' ... which is the same as saying that 'some even integers are even'.

However, 'no even integers are odd' can be understood as 'all even integers are not odd', and so it should be:

$\forall x ( (E(x) \land I(x)) \rightarrow \neg E(x) )$