The trees always blossom in May if April rainfall exceeds 5 centimeters. If April rainfall exceeds 5 centimeters, the...

Nina July 1, 2014

Answer choice A over C

I am having trouble distinguishing why the answer is A and not C. I have diagrammed the following for the problem: P: AR<5cm - > TBM Not TBM - > Not AR<5cm P:AR<5cm - > RFmay1 Not RFmay1 - > Not AR<5cm ________________________________ C: Not RFmay1 - > Not TBM I see that the flaw is that you cannot simply jump back from Not RFmay1 to TBM because you are jumping back from a sufficient premise. I diagrammed Answer choice A) as follows: P: GP - > F Not GP - > Not F P: GP - >PBS Not PBS - > Not GP _____________________ C: Not F - > Not PBS I see how this could be correct... However I diagrammed answer choice C has the same flaw : C) P: B<200 - > special Not special - > Not B<200 P: WT - > B<200 Not WT - > Not B<200 __________________________ C: Not special - > Not WT Where did I go wrong? Also when you have terms like greater than and less then can the contra positive of those be for example Not B<200 or less than?

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Naz July 7, 2014

Your issue is in your contrapositives. Always remember to negate and SWITCH both sides. Let's diagram the problem together.

"The trees always blossom in May if April rainfall exceeds 5 centimeters."

PR1: AR>5 ==> TBM

not TBM ==> not AR>5

"If April rainfall exceeds 5 centimeters, then the reservoirs are always full on May 1."

PR2: AR>5 ==> RFM1

not RFM1 ==> not AR>5

"The reservoirs were not full this May"

P: not RFM1

"Thus the trees will not blossom this May."

C: not TBM

The flaw is that we are concluding "not TBM" from "not RFM1," when all we can deduce from "not RFM1" is "not AR>5."

"Not AR>5" is the necessary condition for the contrapositive of the first principle rule; so we cannot conclude anything further. Rather, the argument is using the necessary condition "not AR>5" to conclude the sufficient condition "not TBM."

Now, let's diagram answer choice (A).

"If the garlic is in the pantry, then it is still fresh."

P1: GP ==> F

not F ==> not GP

"And the potatoes are on the basement stairs if the garlic is in the pantry."

P2: GP ==> PBS

not PBS ==> not GP

"The potatoes are not on the basement stairs."

P: not PBS

"So the garlic is not still fresh."

C: not F

Here we are faced with the exact same flaw. Just as in the argument, we are presented with the sufficient condition of the contrapositive of the second principle rule. From that we can conclude "not GP," which is also the necessary condition of the contrapositive of the first principle rule. Answer choice (A), just like the argument, uses this necessary condition to deduce the sufficient condition: "not F." We cannot deduce anything from a necessary condition. So, answer choice (A) and the stimulus have the same exact flawed pattern of reasoning.

Now, let's look at answer choice (C).

"A book is classified 'special' if it is more than 200 years old."

P1: B>200 ==> S

not S ==> not B>200

"If a book was set with wooden type, then it is more than 200 years old."

P2: WT ==> B>200

not B>200 ==> not WT

"This book is not classified 'special.'"

P: not S

"So it is not printed with wooden type."

C: not WT

If we have the variable "not S," then we know, according to the contrapositive of the first principle rule that we can deduce "not B>200." From there we can use the contrapositive of the second principle rule to deduce "not WT." The deduction looks like this: not S ==> not B>200 ==> not WT. Therefore, answer choice (C) is not flawed. It is a valid contrapositive transitive argument.

Hope that was helpful! Please let us know if you have any other questions.