1. The problem statement, all variables and given/known data Find a counter example to show that the following is invalid: ∃xP(x) ∧ ∃x(P(x) → Q(x)) → ∃xQ(x) 2. Relevant equations - 3. 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". So: 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..