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

izyat June 21, 2019

Question seems like a valid contrapostive statement

When I tried to solve this question, I seemed to find that it had a valid contrapositive argument, but the question says it is flawed. Would it be possible to get an explanation for why it is flawed?

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tylermtakeshita July 11, 2019

I had the same issue. Notice in the first sentence, the "If" indicating the sufficient condition comes before "April rainfall exceeds 5 centimeters". This means that "trees always blossom would be the necessary condition instead of the sufficient as I (and I think you must have) originally diagrammed it.

Ravi July 11, 2019

@izyat and @noname,

Happy to help. Let's take a look.

Here's how we can diagram the stimulus:

ARE5 - >TAB
ARE5 - >RFM1

/RFM1

Therefore, /TAB

This is not a valid contrapositive. The argument's structure is

A - >B
A - >C

not C

Therefore, not B

This is incorrect. with /RFM1, we can conclude that /ARE5 (the failure
of the sufficient condition). However, for the rule

ARE5 - >TAB, if the sufficient condition is failed, we cannot conclude
/TAB, which is what the argument mistakenly concludes. This is why the
argument is flawed.

We see the same type of flaw in (A)

GP - >SF
GP - >PBS

/PBS

Therefore, /SF

A - >B
A - >C

not C

Therefore, not B

Sure, /PBS invokes /GP, but /GP does not invoke /SF.

Does this make sense? Let us know if you have any other questions!