Translate the following inference to logic notation: For all x, if x were a cashier, then x is bored. There is at least one x for which if x were bored, then x is a scientist. For all x, if x were a scientist, then x is a cashier. Therefore there is at least one x for which if x were a scientist, then x is bored.
forall x: P(x) -> Q(x). exists x: Q(x) -> R(x). forall x: R(x) -> P(x). Therefore exists x: R(x) -> Q(x).