Translate the following inference to logic notation: For all x, x_11 is happy if and only if x_11 will play a game. For all x, if x_11 were a nurse, then x_11 is playing a game. For all x, if x_11 were happy, then x_11 is a nurse. Therefore if John were happy, then John is a nurse.
forall x: P(x) <-> Q(x). forall x: R(x) -> Q(x). forall x: P(x) -> R(x). Therefore P(a) -> R(a).