Translate the following inference to logic notation: For all x, x_6 is fast if and only if x_6 will write a letter. There is at least one x for which if x_6 goes running, then x_6 is fast. For all x, x_6 will write a letter. Therefore there is at least one x for which x_6 is fast.
forall x: P(x) <-> Q(x). exists x: R(x) -> P(x). forall x: Q(x). Therefore exists x: P(x).