Amateur Astronomer: Once the sun sets, it gets colder. ... ...

If the amateur astronomer's statements are true, which of the following can be concluded?
(A) It is not as cold as it could be.
(B) ...
(C) ...
(D) ...
(E) ...

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

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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.
 
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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.