Translate the following inference to logic notation: For all x, x_7 is a poet if and only if x_7 is a carpenter. There is at least one x for which x_7 is a nurse. For all x, if x_7 were a nurse, then x_7 is a poet. Therefore there is at least one x for which x_7 is a carpenter.
forall x: P(x) <-> Q(x). exists x: R(x). forall x: R(x) -> P(x). Therefore exists x: Q(x).