Translate the following inference to logic notation: There is at least one x for which x_7 is a cashier. For all x, x_7 is fast or x_7 is not a carpenter. For all x, if x_7 were a cashier, then x_7 is a carpenter. Therefore there is at least one x for which x_7 is fast.
exists x: P(x). forall x: Q(x) or ~R(x). forall x: P(x) -> R(x). Therefore exists x: Q(x).