Translate the following inference to logic notation: For all x, if x_10 were a carpenter, then x_10 is a lawyer. For all x, if x_10 were a lawyer, then x_10 is a carpenter. There is at least one x for which x_10 is a carpenter if and only if x_10 is a lawyer. Therefore there is at least one x for which x_10 is a lawyer if and only if x_10 is a carpenter.
forall x: P(x) -> Q(x). forall x: Q(x) -> P(x). exists x: P(x) <-> Q(x). Therefore exists x: Q(x) <-> P(x).