Sufficient & Necessary Questions - - Question 9

If a society encourages freedom of thought and expression, then, during the time when it does so, creativity will flo...

hectorg December 27, 2019

compound

isnt the first sentence a compound sufficent it has and freedom of thought and expression

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Skylar December 29, 2019

Maybe I can help.

Yes, we could write the first sentence as a compound Sufficient condition, but the compound variables are so closely related that they could be also combined and written as "encourage freedom" without changing the argument. Ultimately, whether or not the first sentence is written as a compound does not change the error in the passage or the answer to the question.

To understand this, let's breakdown the passage using a compound Sufficient condition:

If a society encourages freedom of thought (EFT) and encourages freedom of expression (EFE), then creativity will flourish (CF). An example of creativity flourishing in the 18th century United States is offered, and it is concluded that freedom of thought existed then and there.

EFT and EFE -> CF
CF
____
EFT

The significant error here is that the Necessary condition (CF) is used to conclude (at least part of) the Sufficient condition (EFT). So, the S->N statement is only reversed. This is the same flaw in seen in answer choices (A) - (D).

Now, let's breakdown (E):

If a country is democratic (D), then the opinion of each citizen will have a meaningful effect on government (ME). In none of the Western countries does each citizen's opinion have such an effect, so it is concluded that none of the Western countries are democratic.

D -> ME
NOT ME
_______
NOT D

This is a valid use of the contrapositive. Whereas the passage only reverses the original S->N statement, (E) reverses AND negates It. Therefore, (E) does not make the same error as the passage does and must be correct.

Does that make sense? Please let us know if you have any other questions.

Brett-Lindsay July 4, 2020

That's great, @Skylar. I've been mulling over this question of compounding.

I had simply combined "thought and expression" into one idea, because they both seem to be subordinate to "freedom of"

"If a society encourages freedom of [thought and expression]"

While it's grammatically sound, I'm not really sure if that's really logically sound, and I'm sure that there would be numerous exceptions.


When thinking about the contrapositive, would we be able to look at compound statements by breaking them into two statements?

EFT and EFE --> CF
not CF --> not EFT or not EFE

I know we can't do this to the positive statement, but could we view the contrapositive as two separate statements? After all, it only takes one necessary condition (either not EFT or not EFE) to negate the sufficient (not CF).

either
not CF --> not EFT
or
not CF --> not EFE

It seems to work, but would it be applicable?

Thanks.

Dez March 15, 2021

This made sense perfectly. I had the same question and was confused when I watched the video because the video diagrammed the question differently. Now that I've seen the question diagrammed in both ways, I am able to have a better understanding.