Translate the following inference to logic notation: Barbara is a janitor if and only if William is writing a letter. For all x, x_17 is excited if and only if x_17 will write a letter. It is late. If William were excited, then it is not late. Therefore Barbara is not a janitor.
p <-> P(a). forall x: Q(x) <-> P(x). q. Q(a) -> ~q. Therefore ~p.