Translate the following inference to logic notation: For all x, if y listens to a song, then y is an astronaut. Joseph is listening to a song or James is not excited. For all x, if y were an astronaut, then y is a taxi driver. Therefore if James were excited, then Joseph is a taxi driver.
forall x: P(x) -> Q(x). P(a) or ~p. forall x: Q(x) -> R(x). Therefore p -> R(a).