Translate the following inference to logic notation: For all x, if x_7 were a bartender, then x_7 is a mechanic. For all x, x_7 is a police officer or x_7 will not write a letter. There is at least one x for which if x_7 were a mechanic, then x_7 is writing a letter. Therefore there is at least one x for which if x_7 were a bartender, then x_7 is a police officer.
forall x: P(x) -> Q(x). forall x: R(x) or ~S(x). exists x: Q(x) -> S(x). Therefore exists x: P(x) -> R(x).