Translate the following inference to logic notation: For all x, if z_3 were bored, then z_3 is writing a letter. If Susan were an artist, then Jennifer is bored. If Jennifer writes a letter, then Susan is an artist. Therefore Jennifer is bored if and only if Susan is an artist.
forall x: P(x) -> Q(x). p -> P(a). Q(a) -> p. Therefore P(a) <-> p.