Translate the following inference to logic notation: There is at least one x for which if x_1 were a lawyer, then x_1 is a musician. For all x, x_1 is a musician if and only if x_1 is a writer. For all x, if x_1 were a writer, then x_1 is a lawyer. Therefore there is at least one x for which x_1 is a lawyer if and only if x_1 is a musician.
exists x: P(x) -> Q(x). forall x: Q(x) <-> R(x). forall x: R(x) -> P(x). Therefore exists x: P(x) <-> Q(x).