Translate the following inference to logic notation: For all x, if x_4 were sad, then x_4 is writing a letter. For all x, x_4 is fast if and only if x_4 will write a letter. Therefore for all x, if x_4 were sad, then x_4 is fast.
forall x: P(x) -> Q(x). forall x: R(x) <-> Q(x). Therefore forall x: P(x) -> R(x).