Translate the following inference to logic notation: If Patricia were a janitor, then Thomas is listening to a song. Thomas is not rich. For all x, x_21 will listen to a song if and only if x_21 is rich. Patricia is a janitor if and only if Charles is sad. Therefore Charles is not sad.
p -> P(a). ~Q(a). forall x: P(x) <-> Q(x). p <-> q. Therefore ~q.