Translate the following inference to logic notation: There is at least one x for which y_3 will write a letter. For all x, if y_3 were a carpenter, then y_3 is a soldier. For all x, if y_3 were a soldier, then y_3 is writing a letter. For all x, if y_3 writes a letter, then y_3 is a soldier. Therefore there is at least one x for which y_3 is a soldier.
exists x: P(x). forall x: Q(x) -> R(x). forall x: R(x) -> P(x). forall x: P(x) -> R(x). Therefore exists x: R(x).