Translate the following inference to logic notation: For all x, if y_3 were a mechanic, then y_3 is writing a letter. For all x, if y_3 writes a letter, then y_3 is a mechanic. For all x, if y_3 writes a letter, then y_3 is a mechanic. Therefore for all x, y_3 will write a letter if and only if y_3 is a mechanic.
forall x: P(x) -> Q(x). forall x: Q(x) -> P(x). forall x: Q(x) -> P(x). Therefore forall x: Q(x) <-> P(x).