Translate the following inference to logic notation: For all x, y is not curious. There is at least one x for which y is curious if and only if y will sleep. For all x, y is sad if and only if y will write a letter. For all x, y will sleep if and only if y will write a letter. Therefore there is at least one x for which y is not sad.
forall x: ~P(x). exists x: P(x) <-> Q(x). forall x: R(x) <-> S(x). forall x: Q(x) <-> S(x). Therefore exists x: ~R(x).