I know this statement is not always true, but I'm having a hard time proving it.
I'm also wondering what the difference between:
$[\exists x \in U, P(x)] \implies [\forall x \in U, P(x)]$
$[\exists x \in U, P(x)] \implies [\forall y \in U, P(y)]$
For the first one, when I try to negate it and show that the negation is true, I end up with something like:
$[\exists x \in U, P(x)] \land [\exists x \in U, \lnot P(x)]$,
but if it was written as the second one I could just provide some counterexample y...?
Or am I just not parsing the statement correctly?
Thanks in advance!