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