Translate the following inference to logic notation: For all x, if x_8 writes a letter, then x_8 is a musician. For all x, if x_8 were a mechanic, then x_8 is writing a letter. There is at least one x for which x_8 is a musician if and only if x_8 is a mechanic. Therefore there is at least one x for which if x_8 were a musician, then x_8 is a mechanic.
forall x: P(x) -> Q(x). forall x: R(x) -> P(x). exists x: Q(x) <-> R(x). Therefore exists x: Q(x) -> R(x).