Translate the following inference to logic notation: There is at least one x for which y is a musician if and only if y will take a plane. For all x, if y were a carpenter, then y is a musician. For all x, y will not take a plane. For all x, if y were a musician, then y is a carpenter. Therefore there is at least one x for which y is not a carpenter.
exists x: P(x) <-> Q(x). forall x: R(x) -> P(x). forall x: ~Q(x). forall x: P(x) -> R(x). Therefore exists x: ~R(x).