Discussion
If the amateur astronomer's statements are true, which of the following can be concluded?
*This question is included in Exercise Set 2: Intro to Negation, question #4
| (A) | It is not as cold as it could be. |
| (B) | ... |
| (C) | ... |
| (D) | ... |
| (E) | ... |
| (F) | ... |
The solution is
Posted: 08/30/2011 07:15
I chose D. I don't understand. If it hasn't gotten colder, then the sun hasn't set and the stars aren't out.
Posted: 08/30/2011 14:15
Here is the diagram of the passage:
SS --> Colder
SS --> SV
You know it has NOT gotten colder, as this is stated in the passage. So you have "~Colder".
The contrapositive of the first conditional is:
~Colder --> ~SS
So, since we know that it has not gotten colder, we know that the sun has not set.
Thus, answer choice "C" is correct.
'Why isn't "D" correct?':
We know that the temp has not dropped. But what about the stars? Well, we know:
SS --> SV
And we know that the sun has not yet set. This means we have:
~SS
But we CANNOT take these two pieces of info and conclude that the stars are not visible. To do so would require us to assume:
~SS --> ~SV
This is the INVERSE ERROR.
SS --> Colder
SS --> SV
You know it has NOT gotten colder, as this is stated in the passage. So you have "~Colder".
The contrapositive of the first conditional is:
~Colder --> ~SS
So, since we know that it has not gotten colder, we know that the sun has not set.
Thus, answer choice "C" is correct.
'Why isn't "D" correct?':
We know that the temp has not dropped. But what about the stars? Well, we know:
SS --> SV
And we know that the sun has not yet set. This means we have:
~SS
But we CANNOT take these two pieces of info and conclude that the stars are not visible. To do so would require us to assume:
~SS --> ~SV
This is the INVERSE ERROR.