Translate the following inference to logic notation: For all x, x_6 is not a scientist or x_6 will play tennis. There is at least one x for which x_6 is a scientist or x_6 is a mechanic. For all x, x_6 will play tennis if and only if x_6 is a cashier. For all x, if x_6 were a mechanic, then x_6 is a cashier. Therefore there is at least one x for which x_6 is a cashier.
forall x: ~P(x) or Q(x). exists x: P(x) or R(x). forall x: Q(x) <-> S(x). forall x: R(x) -> S(x). Therefore exists x: S(x).