Translate the following inference to logic notation: There is at least one x for which if x writes a letter, then x is a scientist. For all x, x is a scientist if and only if x is a police officer. For all x, x is a police officer. Therefore there is at least one x for which x is a scientist.
exists x: P(x) -> Q(x). forall x: Q(x) <-> R(x). forall x: R(x). Therefore exists x: Q(x).