Translate the following inference to logic notation: There is at least one x for which x_7 is a doctor or x_7 will sleep. For all x, x_7 is not a server. For all x, if x_7 were a doctor, then x_7 is taking a plane. For all x, x_7 is a server if and only if x_7 will take a plane. Therefore there is at least one x for which x_7 will sleep.
exists x: P(x) or Q(x). forall x: ~R(x). forall x: P(x) -> S(x). forall x: R(x) <-> S(x). Therefore exists x: Q(x).