Translate the following inference to logic notation: For all x, x_12 is poor. There is at least one x for which if x_12 were poor, then x_12 is a cashier. For all x, x_12 will write a letter and x_12 will sleep. Therefore there is at least one x for which x_12 is a cashier and x_12 will write a letter.
forall x: P(x). exists x: P(x) -> Q(x). forall x: R(x) and S(x). Therefore exists x: Q(x) and R(x).