Translate the following inference to logic notation: For all x, if x_2 were a politician, then x_2 is not writing a letter. For all x, x_2 is a musician. For all x, if x_2 were a musician, then x_2 is writing a letter. There is at least one x for which x_2 is a politician or x_2 will go running. Therefore there is at least one x for which x_2 will go running.
forall x: P(x) -> ~Q(x). forall x: R(x). forall x: R(x) -> Q(x). exists x: P(x) or S(x). Therefore exists x: S(x).