Translate the following inference to logic notation: There is at least one x for which x_15 is a carpenter if and only if x_15 is an artist. For all x, if x_15 were a carpenter, then x_15 is a doctor. For all x, x_15 is an artist if and only if x_15 is a doctor. Therefore there is at least one x for which if x_15 were a carpenter, then x_15 is an artist.
exists x: P(x) <-> Q(x). forall x: P(x) -> R(x). forall x: Q(x) <-> R(x). Therefore exists x: P(x) -> Q(x).