Translate the following inference to logic notation: For all x, if x_15 listens to a song, then x_15 is a scientist. Thomas is a soldier or Karen is taking a plane. If Thomas were a soldier, then Joseph is listening to a song. Joseph is a scientist if and only if Karen is taking a plane. Therefore Joseph is a scientist.
forall x: P(x) -> Q(x). p or q. p -> P(a). Q(a) <-> q. Therefore Q(a).