Translate the following inference to logic notation: For all x, if x_10 listens to a song, then x_10 is climbing a mountain. If Richard sleeps, then Patricia is listening to a song. If it is overcast, then Richard is sleeping. Therefore if it is overcast, then Patricia is climbing a mountain.
forall x: P(x) -> Q(x). p -> P(a). q -> p. Therefore q -> Q(a).