Translate the following inference to logic notation: For all x, x_7 will drink water if and only if x_7 will play a game. For all x, x_7 is a nurse or x_7 will drink water. For all x, if x_7 were a nurse, then x_7 is playing a game. There is at least one x for which x_7 is a mechanic. Therefore there is at least one x for which x_7 will play a game and x_7 is a mechanic.
forall x: P(x) <-> Q(x). forall x: R(x) or P(x). forall x: R(x) -> Q(x). exists x: S(x). Therefore exists x: Q(x) and S(x).