The correct answer to this question is False. Murder is a mortal sin when one does it voluntarily with no reasoning other than the point of wanting to kill them. In the example provided, the soldier is defending himself. Under religion, we all can protect ourselves against harm, and being that he is protecting himself, the soldier is not in the wrong for killing his enemy. Regardless of the reason, he did still kill someone.
Though it is not a mortal sin, the soldier should still speak with God about what occurred and deal with any emotions he has about the killing.
While the soldier has killed another person, he had not committed a mortal sin provided that he killed the person in self-defense. He has the right to defend his own life even at the expense of the other because we are called to respect ourself and preserve our own life.