Find a counter example to show that the following is invalid:
∃xP(x) ∧ ∃x(P(x) → Q(x)) → ∃xQ(x)
The Attempt at a Solution
Well, I have tried to find something related to properties of numbers but found nothing... Then I tried to mess around with some nonsense sentences like:
Let x be a creature, P(x) = "x is human being", Q(x) = "x is male".
Some creature is human being - true
For some creature if it is human being then it is male. - true
Some creature it is a male - true
(true and true) = true
(true → true) = true
So no counter example here. Any hint for me? I'm pretty much stuck..