Translate the following inference to logic notation: For all x, x_6 will write a letter if and only if x_6 is an office clerk. For all x, if x_6 listens to a song, then x_6 is writing a letter. For all x, if x_6 were an office clerk, then x_6 is listening to a song. Therefore for all x, if x_6 writes a letter, then x_6 is an office clerk.
forall x: P(x) <-> Q(x). forall x: R(x) -> P(x). forall x: Q(x) -> R(x). Therefore forall x: P(x) -> Q(x).