Translate the following inference to logic notation: For all x, if x_6 sleeps, then x_6 is writing a letter. For all x, x_6 is not a mechanic or x_6 will play tennis. For all x, x_6 will play tennis if and only if x_6 will write a letter. There is at least one x for which x_6 is a mechanic or x_6 will sleep. Therefore there is at least one x for which x_6 will write a letter.
forall x: P(x) -> Q(x). forall x: ~R(x) or S(x). forall x: S(x) <-> Q(x). exists x: R(x) or P(x). Therefore exists x: Q(x).