Translate the following inference to logic notation: For all x, x_9 will not write a letter. For all x, if x_9 were a musician, then x_9 is an artist. For all x, if x_9 were an artist, then x_9 is cooking. There is at least one x for which x_9 will write a letter if and only if x_9 will cook. Therefore there is at least one x for which x_9 is not a musician.
forall x: ~P(x). forall x: Q(x) -> R(x). forall x: R(x) -> S(x). exists x: P(x) <-> S(x). Therefore exists x: ~Q(x).