Discussion
If the pundit's statements are true, which of the following can be concluded?
*This question is included in Exercise Set 2: Intro to Negation, question #12
| (A) | There is no asset bubble. |
| (B) | ... |
| (C) | ... |
| (D) | ... |
| (E) | ... |
| (F) | ... |
The solution is
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!
"it's not true" means the condition "IL" is not true or the result "~AB" is not true or neither true?
Thanks!
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
IL -> ~(~AB)
The double negatives cancel each other.
IL -> AB
Posted: 04/21/2012 09:50
The 2nd part of the 2nd sentence can be diagrammed:
AB --> Bubble indications.
Or
~ bubble indicators --> ~ asset bubble.
AB --> Bubble indications.
Or
~ bubble indicators --> ~ asset bubble.
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?
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?
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.
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.
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.
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.