Political Pundit: It's not true that if the Federal Reserve ... ...

If the pundit's statements are true, which of the following can be concluded?
(A) There is no asset bubble.
(B) ...
(C) ...
(D) ...
(E) ...

*This question is included in Exercise Set 2: Intro to Negation

 
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Posted: 04/21/2012 03:48
Could anyone tell me how to make sign on" it's not true that... will not develop"? Should it be "~IL--- ~AB" or "~IL--- AB"? Why?
"it's not true" means the condition "IL" is not true or the result "~AB" is not true or neither true?
Thanks!
Arcadia
Admin
 
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Posted: 04/21/2012 09:41
First, rearrange the statement: if the feds chairman keeps interest rates low for a decade, it's not true that an asset bubble will not develop.

IL -> ~(~AB)
The double negatives cancel each other.
IL -> AB
Arcadia
Admin
 
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Posted: 04/21/2012 09:50
The 2nd part of the 2nd sentence can be diagrammed:
AB --> Bubble indications.
Or
~ bubble indicators --> ~ asset bubble.
 
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Posted: 05/01/2012 21:35
Admin,

Your post said that we can conclude that IL --> AB. So then we should be able to also conclude that ~AB --> ~IL. Or in other words if there is no asset bubble, then interest rates are not low.

We know that ~AB from the passage.

Choice C says "It is not true that interest rates have been kept excessively low." which is ~IL. So since ~AB --> ~IL, then why can this not be concluded?
Contributor
 
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Posted: 05/03/2012 13:20
Dan, thanks for asking a very good question.

Mr. Admin was not supposed to re-arrange "It's not true that if the Federal Reserve chairman keeps interest rates excessively low for a decade, an asset bubble will not develop." into "If the ..., it's not true that ..." because it changes the meaning of the premise. The rearrangement is diagrammed as IL -> ~(~AB) and indeed it would mean ~AB --> ~IL, it was incorrect to rearrange it in the first place.

The correct diagram for "It's not true that if the Federal Reserve chairman keeps interest rates excessively low for a decade, an asset bubble will not develop." is as follows:

Shorthand:
~(IL --> ~AB)

This can be rewritten:
IL + ~~AB
-or-
IL + AB

Hence, we cannot conclude C from the information given.

However, we can conclude A from the 2nd premise.
 
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Posted: 05/03/2012 16:47
What's to say there is no asset bubble? If the first statement is not true, there still could or could not be an asset bubble.
Contributor
 
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Posted: 05/03/2012 18:40
Sawan, indeed. We can't conclude there is no asset bubble from the first premise. But from the 2nd premise, we can.