You are absolutely correct that this is a Justify the Conclusion (or a sufficient
assumption question.) In this case, the missing information that would prove the conclusion is a conditional relationship, which by definition includes both a sufficient and a necessary condition. So don't dismiss the answer choice because it contains a necessary condition indicator. Consider the entire context
of the answer choice to see if it matches.
Your prephrase was strong, and this is a very straightforward Justify question for which the prephrase is both mechanical and devastating. Here's how I would diagram the argument:
MP = mathematical proposition
PTO = proven true by observation
KT = known to be true
Your prephrase is that the correct answer choice will link to together the two previously unconnected portions of the argument, in this case PTO
, in a way that proves the conclusion KT
is valid. In other words, the correct answer choice will say:
Since the prephrased link between the premise and the conclusion is a conditional relationship, it will have both a sufficient and a necessary condition.
Answer choice (D) is incorrect because it states the Mistaken Reversal of our prephrase, and the Mistaken Negation of the relationship as stated in answer choice (E). This answer choice would be diagrammed as:
Answer choice (E) contains the logical equivalent of our prephrase, though it is stated in terms of the contrapositive:
Hope that helps!