Translate the following inference to logic notation: For all x, if x_8 were bored, then x_8 is a nurse. There is at least one x for which x_8 is a soldier. For all x, x_8 is a nurse if and only if x_8 is a poet. For all x, x_8 is bored or x_8 is a poet. Therefore there is at least one x for which x_8 is a nurse and x_8 is a soldier.
forall x: P(x) -> Q(x). exists x: R(x). forall x: Q(x) <-> S(x). forall x: P(x) or S(x). Therefore exists x: Q(x) and R(x).