A syllogistic fallacy is more of a generalization than it is a sequence or analogy. This error of reasoning occurs by first mentioning something broad/general then proceeds to make a conclusion about something that is very specific by means of generalizing. For example, this would be considered fallacy of syllogism:
All jets are air crafts. All propeller airplanes are air crafts. Therefore, propeller airplanes are jets.
Thus, you can see how a generalization is made about propeller airplanes being jets because they are both air crafts.
The answer is the amputation of the lieutenant's arm. None of the other options are events in the story. The lieutenant returns home and we don't know the outcome of the battle. There is also no evidence he was ever ill.