You seem to be mixing up two approaches: you're using both existential quantification and also material implication, when you only need one.
Is this homework? You should try to figure it out on your own (and also not be posting the questions online).
If not, if you just want to talk about the ideas behind predicate logic, we can discuss it here, but be aware this will NOT necessarily result in the "right" answers for your class which will use one specific approach that won't be the same as other classes or what people on the internet say.