Translate the following inference to logic notation: For all x, if x_15 were an artist, then x_15 is writing a letter. For all x, x_15 will play tennis if and only if x_15 will climb a mountain. For all x, if x_15 climbs a mountain, then x_15 is an artist. There is at least one x for which if x_15 writes a letter, then x_15 is playing tennis. Therefore there is at least one x for which if x_15 climbs a mountain, then x_15 is an artist.
forall x: P(x) -> Q(x). forall x: R(x) <-> S(x). forall x: S(x) -> P(x). exists x: Q(x) -> R(x). Therefore exists x: S(x) -> P(x).