Translate the following inference to logic notation: For all x, x_4 is bored or x_4 will cook. For all x, if x_4 cooks, then x_4 is working. There is at least one x for which x_4 is bored if and only if x_4 will work. Therefore there is at least one x for which x_4 will work.
forall x: P(x) or Q(x). forall x: Q(x) -> R(x). exists x: P(x) <-> R(x). Therefore exists x: R(x).