Translate the following inference to logic notation: For all x, x_12 is curious if and only if x_12 is a nurse. There is at least one x for which x_12 will write a letter or x_12 is not curious. For all x, if x_12 writes a letter, then x_12 is a nurse. Therefore there is at least one x for which x_12 is a nurse if and only if x_12 is curious.
forall x: P(x) <-> Q(x). exists x: R(x) or ~P(x). forall x: R(x) -> Q(x). Therefore exists x: Q(x) <-> P(x).