Translate the following inference to logic notation: There is at least one x for which x_9 is a politician if and only if x_9 is a cashier. For all x, x_9 will not climb a mountain. For all x, x_9 will climb a mountain or x_9 will write a letter. For all x, if x_9 writes a letter, then x_9 is a cashier. Therefore there is at least one x for which x_9 is a cashier.
exists x: P(x) <-> Q(x). forall x: ~R(x). forall x: R(x) or S(x). forall x: S(x) -> Q(x). Therefore exists x: Q(x).