Translate the following inference to logic notation: For all x, x_12 is a nurse. There is at least one x for which x_12 is a janitor. For all x, x_12 is a nurse if and only if x_12 will write a letter. 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 janitor and x_12 will write a letter.
forall x: P(x). exists x: Q(x). forall x: P(x) <-> R(x). forall x: R(x) -> P(x). Therefore exists x: Q(x) and R(x).