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