Translate the following inference to logic notation: For all x, x_15 is a nurse if and only if x_15 is happy. For all x, if x_15 goes running, then x_15 is happy. For all x, x_15 will write a letter or x_15 will go running. For all x, x_15 is an astronaut if and only if x_15 will write a letter. For all x, if x_15 were an astronaut, then x_15 is a nurse. Therefore for all x, x_15 is happy.
forall x: P(x) <-> Q(x). forall x: R(x) -> Q(x). forall x: S(x) or R(x). forall x: T(x) <-> S(x). forall x: T(x) -> P(x). Therefore forall x: Q(x).