Truth value of a proposition I'm trying to write a function in Python that takes it argument as a Python list and returns a boolean value based on the truth vale of the proposition $E(x) \to \exists y \text{ s.t. } x=2y$, where here the proposition $E(x)$ means 'x is even'.

print(check_prop([-2,-1,0,1,2,3])) gives an output true

print(check_prop([-2,-1,0,1,3,4])) gives an output false


I don't quite understand how the truth value is true in the first case and false in the second.
The predicate whose truth value you're trying to check states the following:


  For every even number $x$ in the list, $x/2$ is also in the list.


This holds in the first case: the even numbers are $-2,0,2$, and indeed $-1,0,1$ are in the list, but not in the second case, since $4$ is in the list but $2$ isn't.