Translate the following inference to logic notation: For all x, z is not a mechanic or z will play a game. There is at least one x for which z is a mechanic or z will write a letter. For all x, z will not write a letter. Therefore there is at least one x for which z will play a game or z will work.
forall x: ~P(x) or Q(x). exists x: P(x) or R(x). forall x: ~R(x). Therefore exists x: Q(x) or S(x).