Translate the following inference to logic notation: For all x, if x_4 climbs a mountain, then x_4 is writing a letter. For all x, if x_4 writes a letter, then x_4 is climbing a mountain. For all x, if x_4 climbs a mountain, then x_4 is writing a letter. Therefore for all x, x_4 will climb a mountain if and only if x_4 will write a letter.
forall x: P(x) -> Q(x). forall x: Q(x) -> P(x). forall x: P(x) -> Q(x). Therefore forall x: P(x) <-> Q(x).