#4 - Only if the electorate is moral and intelligent will

[Administrator]

Complete Question Explanation

Must Be True-SN. The correct answer choice is (C)

This stimulus presents a simple conditional statement. We know that “only if” introduces the necessary variable, so we can diagram this statement as follows:

• Moral
  
  DFW +
  
  Intelligent

When we note such a clear example of conditional reasoning, we should draw the contrapositive as well. That is, if there is no morality, or no intelligence, amongst the electorate, the democracy will not function well:

• Moral
  
  or DFW
  
  Intelligent

This is a Must Be True question, so the correct answer choice must be supported by what we have read in the stimulus.

Answer choice (A): This is a Mistaken Reversal of the statement in the stimulus. The original statement claims that if democracy is to function well, there must be a moral and intelligent electorate.

Answer choice (B): It is not known what must be true if a democracy does not function well, only what must be true if a democracy does function well. Also, there is no indication that one situation or the other must happen, but instead that if democracy functions well there must be a moral and intelligent electorate.

Answer choice (C): This is the correct answer choice. If it is not true that the electorate is both moral and intelligent, then the democracy cannot function well. This is the Contrapositive of the original statement and is thus the correct answer.

Answer choice (D): Again, nothing is known about what must be true if the democracy does not function well, only what must be true if it is to function well. This is a Mistaken Negation of the original statement because it negates the sufficient and necessary conditions without reversing them.

Answer choice (E): This is the same Mistaken Reversal error as in answer (A). The answer choice could be restated as: if the electorate is moral and intelligent, then it must be true that a democracy will function well. In this form it is more obvious that the sufficient and necessary conditions have been mislabeled.

[siegelne]

Hello, I'm a bit confused about the question "Only if the electorate is moral and intelligent will a democracy function well." I understand why the answer, C, ("If the electorate is not moral or not intelligent, then a democracy will not function well") is correct, but I don't understand why answer choice D ("If a democracy does not function well, then the electorate is not moral or not intelligent") is wrong?

Moral + Intelligent --> democracy functions well

What is wrong with saying:
democracy does not function well --> either not moral or not intelligent or both?

Thank you

[Steve Stein]

Hi,

The term "only if" is a necessary condition indicator. The conditional statement, re-ordered, would read:
A democracy will function well only if the electorate is moral and intelligent.

This would be diagrammed as:
moral electorate
Function well and
intelligent electorate

On the contrapositive side, if either morals or intelligence is lacking in the electorate, that guarantees that a democracy will not function well:

NOT moral
or NOT function well
NOT intelligent

Let me know whether that clears this one up--thanks!

~Steve

[siegelne]

Very helpful, thank you!

[ellenb]

Dear Powerscore,

I just want to know how to diagram correctly answer choice B.

Thanks

Ellen

[Luke Haqq]

You're right to be confused about how to diagram answer choice (B). This is because, unlike the other 4 answer choices, isn't making a conditional if-then statement.

Rather, (B) gives us an either/or statement about what must be true. The stimulus, though, doesn't state whether either is true but instead only gives a conditional statement.

If you wanted a diagram representing it, even though (B) isn't a conditional statement, you could try something like this:

~function well OR ~moral and/or ~intelligent

[ellenb]

Thanks Luke,

I was just thinking more in terms of what I learned in the lesson, about using the either or relationship and diagramming it:

So, if we have Either A or B, we can diagram it as

A-->not B

B-->not A

Accordingly if we have
Either a democracy does not function well or else the electorate is not moral or not intelligent.

Not function well--->not (electorate is not moral or not intelligent)

we also can deduce that

Electorate is not moral or not intelligent-->Not(not function well )
which becomes

Electorate is not moral or not intelligent-->functions well.


Please let me know whether I got it right, I want to make sure I understand and can apply the either or statement and I was just curious whether it applies in this situation and if so whether I have done it right.

Thanks in advance!

Ellen

[BethRibet]

Hi Ellen,

Yes, it appears that you're correctly following the logical format for this type of problem, provided that the problem specifies either this or that, But Not Both. If it is possible for both conditions to be true, then your diagram would not apply.

best,
Beth

[ellenb]

How would I know that I cannot have both? I know for the logic games it is stated, what about LR?

Thanks

Ellen

[Nikki Siclunov]

Hi Ellen,

Let me clarify what Luke and Beth explained earlier. By itself, the "either/or" construction is potentially inclusive of both. Thus, if we have, "I will eat either an apple or a banana," the correct diagram would be:

NOT A B
NOT B A

You can eat both; you just can't eat neither. In other words, you must eat at least one fruit: an apple or a banana, but may eat both as well.

On the other hand, if the statement claims that "I will eat either an apple or a banana, but not both," then the diagram has two elements to it:

"either/or":
NOT A B
NOT B A

"...but not both":
A NOT B
B NOT A

When combined, the diagram for "either A or B, but not both" would look like this:

A NOT B
B NOT A

Does this make sense?