Translate the following inference to logic notation: For all x, if x_12 were a taxi driver, then x_12 is listening to a song. Joseph is a mechanic. John is not listening to a song. For all x, if x_12 listens to a song, then x_12 is a taxi driver. Therefore John is not a taxi driver and Joseph is a mechanic.
forall x: P(x) -> Q(x). p. ~Q(a). forall x: Q(x) -> P(x). Therefore ~P(a) and p.