Translate the following inference to logic notation: If William were sad, then Robert is listening to a song. For all x, x_9 will listen to a song if and only if x_9 will make tea. For all x, x_9 will not make tea. Therefore William is not sad.
p -> P(a). forall x: P(x) <-> Q(x). forall x: ~Q(x). Therefore ~p.