Translate the following inference to logic notation: For all x, x_5 is a carpenter or x_5 will not listen to a song. For all x, if x_5 were rich, then x_5 is listening to a song. For all x, if x_5 were a carpenter, then x_5 is rich. Therefore for all x, x_5 is a carpenter if and only if x_5 will listen to a song.
forall x: P(x) or ~Q(x). forall x: R(x) -> Q(x). forall x: P(x) -> R(x). Therefore forall x: P(x) <-> Q(x).