Translate the following inference to logic notation: For all x, x_12 will play a game or x_12 is excited. For all x, if x_12 were excited, then x_12 is cooking. For all x, if x_12 cooks, then x_12 is excited. There is at least one x for which x_12 will not play a game or x_12 is an electrician. For all x, x_12 will cook if and only if x_12 is an electrician. Therefore there is at least one x for which x_12 will cook.
forall x: P(x) or Q(x). forall x: Q(x) -> R(x). forall x: R(x) -> Q(x). exists x: ~P(x) or S(x). forall x: R(x) <-> S(x). Therefore exists x: R(x).