Translate the following inference to logic notation: For all x, if x_11 were an astronaut, then x_11 is a sailor. For all x, if x_11 were a nurse, then x_11 is an astronaut. For all x, x_11 will sleep if and only if x_11 is an astronaut. There is at least one x for which x_11 is a mechanic. For all x, x_11 is a nurse or x_11 will sleep. Therefore there is at least one x for which x_11 is a mechanic and x_11 is a sailor.
forall x: P(x) -> Q(x). forall x: R(x) -> P(x). forall x: S(x) <-> P(x). exists x: T(x). forall x: R(x) or S(x). Therefore exists x: T(x) and Q(x).