Translate the following inference to logic notation: There is at least one x for which z is a scientist if and only if z is a server. For all x, z is not bored. For all x, z is bored if and only if z is a server. Therefore there is at least one x for which z is not a scientist.
exists x: P(x) <-> Q(x). forall x: ~R(x). forall x: R(x) <-> Q(x). Therefore exists x: ~P(x).