General Question

Metadata's avatar

What is the reasoning behind this logic question?

Asked by Metadata (37points) August 21st, 2014

Can anyone explain the answer to this question below? I know the answer is C, but I don’t understand why. Also, does anyone know of a logic workbook that would have similar questions with answers so I can practice?

#1 Sample Question:

Premises: If housing starts are up this year, lumber sales at Merrihew Lumber should increase and the company, on shaky grounds for the past several years, will not have to declare bankruptcy. If Merrihew does go out of business, United Building Supplies will have increased lumber sales and will phase out their masonry line. Conclusion: If housing starts are down this year, United Building Supplies will not phase out their masonry line.

a. necessarily true.
b. probably, but not necessarily, true.
c. indeterminable, cannot be determined.
d. probably, but not necessarily, false.
e. necessarily false.

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3 Answers

ragingloli's avatar

if housing starts are down, merrihew lumber does not necessarily go out of business.
the question only states explicitly, that ML will not have to declare bankruptcy if housing projects are up.
it does not explicitly state that ML will declare bankruptcy if they are down.
So, if housing projects are down this year, ML might still be in business, or not. This can not be determined.
Thusly, the condition on which UBS’ phasing out of their masonry product palette depends, is unknown and it can not be determined whether or not they will phase out their masonry line.

longgone's avatar

If A, then probably B and thus, probably NOT C.

IF C, then definitely D and E.

If NOT A, then probably C (and thus D and E). But the key word is “probably” – there is no guarantee.

The clue is in the first sentence (“should increase”).

jerv's avatar

Should… if…. those right there are indeterminate enough to eliminate A and E.

There is no real odds given on Merrihew staying in business despite bankruptcy; some companies file and yet continue to stay open (after restructuring). That, and other missing info rule out any “probably”, so B and D are out.

That leaves C.

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