Translate the following inference to logic notation: For all x, if x_9 writes a letter, then x_9 is cooking. For all x, if x_9 cooks, then x_9 is writing a letter. For all x, if x_9 listens to a song, then x_9 is writing a letter. For all x, if x_9 cooks, then x_9 is listening to a song. Therefore for all x, x_9 will write a letter if and only if x_9 will cook.
forall x: P(x) -> Q(x). forall x: Q(x) -> P(x). forall x: R(x) -> P(x). forall x: Q(x) -> R(x). Therefore forall x: P(x) <-> Q(x).