Translate the following inference to logic notation: For all x, x_10 is a doctor if and only if x_10 will climb a mountain. For all x, x_10 will not take a plane. For all x, x_10 will climb a mountain if and only if x_10 will take a plane. For all x, x_10 is not fast or x_10 will listen to a song. For all x, x_10 is fast or x_10 is a doctor. Therefore for all x, x_10 will listen to a song.
forall x: P(x) <-> Q(x). forall x: ~R(x). forall x: Q(x) <-> R(x). forall x: ~S(x) or T(x). forall x: S(x) or P(x). Therefore forall x: T(x).