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#24 - No mathematical proposition can be proven true by

pacer
• Posts: 57
• Joined: Oct 20, 2014
#17606
I thought that this question is asking for an assumption that is sufficient.

I read in some books that when the question states

which of the following is an assumption on which the conclusion depends? - this means that the task is to find a necessary assumption

and when the question read on "The conclusion follows logically if which of the following assumptions is true?" - the task if to find an assumption that is sufficient

Based on this, this question is asking for a sufficient assumption

This argument is assuming that "Observation is the only method for determining truth"

Observation -> truth

which is more in line with choice C

How do you know it is asking for something necessary?
Ron Gore
• PowerScore Staff
• Posts: 220
• Joined: May 15, 2013
#17616
Hi Pacer,

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

P: MP PTO

C: MP KT

Your prephrase is that the correct answer choice will link to together the two previously unconnected portions of the argument, in this case PTO and KT, in a way that proves the conclusion KT is valid. In other words, the correct answer choice will say:

PTO KT

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:

KT PTO

Answer choice (E) contains the logical equivalent of our prephrase, though it is stated in terms of the contrapositive:

KT PTO

Hope that helps!

Ron

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