Translate the following inference to logic notation: There is at least one x for which x_11 is a bartender if and only if x_11 will take a plane. For all x, if x_11 were a bartender, then x_11 is taking a plane. For all x, if x_11 were an artist, then x_11 is a bartender. For all x, if x_11 takes a plane, then x_11 is an artist. Therefore there is at least one x for which x_11 will take a plane if and only if x_11 is a bartender.
exists x: P(x) <-> Q(x). forall x: P(x) -> Q(x). forall x: R(x) -> P(x). forall x: Q(x) -> R(x). Therefore exists x: Q(x) <-> P(x).