Translate the following inference to logic notation: For all x, if x_10 were a doctor, then x_10 is writing a letter. There is at least one x for which x_10 is a doctor or x_10 will go running. For all x, x_10 will climb a mountain. For all x, if x_10 goes running, then x_10 is writing a letter. For all x, if x_10 climbs a mountain, then x_10 is a mechanic. Therefore there is at least one x for which x_10 is a mechanic and x_10 will write a letter.
forall x: P(x) -> Q(x). exists x: P(x) or R(x). forall x: S(x). forall x: R(x) -> Q(x). forall x: S(x) -> T(x). Therefore exists x: T(x) and Q(x).