Translate the following inference to logic notation: John is writing a letter if and only if Patricia is working. Michael is a cashier if and only if John is listening to a song. For all x, if x_15 listens to a song, then x_15 is writing a letter. Patricia is not working. Therefore Michael is not a cashier.
P(a) <-> p. q <-> Q(a). forall x: Q(x) -> P(x). ~p. Therefore ~q.