Translate the following inference to logic notation: For all x, x_10 is a soldier. There is at least one x for which x_10 will write a letter. For all x, if x_10 writes a letter, then x_10 is a poet. Therefore there is at least one x for which x_10 is a poet.
forall x: P(x). exists x: Q(x). forall x: Q(x) -> R(x). Therefore exists x: R(x).