Translate the following inference to logic notation: For all x, if x_4 writes a letter, then x_4 is a mechanic. For all x, x_4 will write a letter or x_4 will go running. For all x, if x_4 goes running, then x_4 is a mechanic. There is at least one x for which x_4 will play tennis. Therefore there is at least one x for which x_4 will play tennis and x_4 is a mechanic.
forall x: P(x) -> Q(x). forall x: P(x) or R(x). forall x: R(x) -> Q(x). exists x: S(x). Therefore exists x: S(x) and Q(x).