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PT #49, Section 2, #7 (formal logic)

*devo*

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PT #49, Section 2, #7 (formal logic)
« on: November 14, 2008, 07:46:45 PM »
So I am having some trouble with formal logic.  Please help.

#7

Inspected -> ~Infected
Thus, Inspected -> Safe

The argument follows logically if which is assumed?

The correct answer is (E), Safe -> ~Infected.  I chose (D), ~Safe -> Infected.

Inspected is the sufficent condition and I am confused about how to link the two necessary conditions.  Choice (E) is derived by linking Safe to ~Infected and choice (D) is derived by linking ~Infected to Safe then taking the contrapositive.  So why is it incorrect to link the statements this latter way?

Brent Dunn

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Re: PT #49, Section 2, #7 (formal logic)
« Reply #1 on: November 14, 2008, 09:01:47 PM »
Your logic as far as the passage goes is correct, but you have mistranslated the answer choices. Look at the placement of the word "ANY" in the sentence. Since "ANY" is functionally synonymous with "IF" what immediately follows it in this case is the sufficient condition. Therefore answer choice D says Infected--> ~Safe, and answer choice E is the one that says ~Infected--> Safe.
It is a little sneaky when they put the conditional indicator word (any) in the middle of the sentence.

*devo*

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Re: PT #49, Section 2, #7 (formal logic)
« Reply #2 on: November 14, 2008, 11:09:22 PM »
Your logic as far as the passage goes is correct, but you have mistranslated the answer choices. Look at the placement of the word "ANY" in the sentence. Since "ANY" is functionally synonymous with "IF" what immediately follows it in this case is the sufficient condition. Therefore answer choice D says Infected--> ~Safe, and answer choice E is the one that says ~Infected--> Safe.
It is a little sneaky when they put the conditional indicator word (any) in the middle of the sentence.

Thanks for the quick response.  I guess it would be important to know that ANY introduces the sufficient condition  :P.

So I see how choice E pops out as the correct answer, but I am trying to understand why D still looks correct as well.  I don't know if this is another mistranslation, but it seems like I could take the contrapositive of Safe -> ~Infected, which is Infected -> ~Safe and this is exactly what answer choice D says. 

Whereas you used the necessary condition of the premise and used it as the sufficient condition of your answer, I used the necessary condition of the conclusion and used it as my sufficient condition (then applied the contrapositive).  I am obviously not allowed to do one of these things. What is it?

EarlCat

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Re: PT #49, Section 2, #7 (formal logic)
« Reply #3 on: November 15, 2008, 12:19:12 AM »
I think you're still misreading something...

TCR should say ~Infected --> Safe.


P: Inspected --> ~Infected
C: Inspected ----------------> Safe
A:               ~Infected --> Safe