Translate the following inference to logic notation: There is at least one x for which y_4 will play a game if and only if y_4 is a doctor. For all x, y_4 will not make tea. For all x, y_4 is a doctor if and only if y_4 will make tea. For all x, if y_4 were a nurse, then y_4 is playing a game. Therefore there is at least one x for which y_4 is not a nurse.
exists x: P(x) <-> Q(x). forall x: ~R(x). forall x: Q(x) <-> R(x). forall x: S(x) -> P(x). Therefore exists x: ~S(x).