Translate the following inference to logic notation: For all x, x_3 will take a plane if and only if x_3 will listen to a song. For all x, x_3 will work if and only if x_3 will listen to a song. For all x, if x_3 works, then x_3 is taking a plane. Therefore for all x, if x_3 takes a plane, then x_3 is working.
forall x: P(x) <-> Q(x). forall x: R(x) <-> Q(x). forall x: R(x) -> P(x). Therefore forall x: P(x) -> R(x).