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