Translate the following inference to logic notation: If James were a soldier, then James is excited. For all x, if x_10 were a soldier, then x_10 is excited. For all x, if x_10 were excited, then x_10 is a soldier. Therefore James is excited if and only if James is a soldier.
P(a) -> Q(a). forall x: P(x) -> Q(x). forall x: Q(x) -> P(x). Therefore Q(a) <-> P(a).