Translate the following inference to logic notation: For all x, x_10 will play tennis if and only if x_10 is an artist. There is at least one x for which if x_10 plays tennis, then x_10 is a cashier. For all x, if x_10 were a cashier, then x_10 is making tea. For all x, if x_10 makes tea, then x_10 is a carpenter. Therefore there is at least one x for which if x_10 were an artist, then x_10 is a carpenter.
forall x: P(x) <-> Q(x). exists x: P(x) -> R(x). forall x: R(x) -> S(x). forall x: S(x) -> T(x). Therefore exists x: Q(x) -> T(x).