Translate the following inference to logic notation: If William were a janitor, then William is an artist. For all x, if x_6 were an artist, then x_6 is writing a letter. For all x, if x_6 writes a letter, then x_6 is a janitor. Therefore William is a janitor if and only if William is an artist.
P(a) -> Q(a). forall x: Q(x) -> R(x). forall x: R(x) -> P(x). Therefore P(a) <-> Q(a).