by stackoutawinner Thu Aug 27, 2009 5:56 pm
Okay, I'm going to attempt to solve the question in real time as I type...
1. economy doing badly
2. RE in a slump
3. Car sales lowest in years
4. If 2 or 3 weren't true, then 1 would be incorrect
5. 1 is true because 2 & 3 are both true
The question is an inference, calling for us to choose the answer that is supported by the above argument.
Answer choice A says because 2, therefore 1. This violates 4. Strike
Answer choice B says If 1, then either 2 or 3. This not only is a fallacy in relation to the argument, but it also goes against 4 (because the argument calls for both). The fallacy committed here is affirming the consequent, but as I said, it doesn't even get that right.
Answer choice C says if no 2, then no 1. This goes along with 4. Therefore, I'm going to say this is correct... but will now check the other two to make sure
Answer choice D says if not 1 then not likely to have both 2 & 3. This is the contrapositive of the argument. The argument says IF 2 & 3 THEN 1. This answer choice says ~ 1 --> ~ 2 v ~ 3. The catch here is the word "unlikely". I'll defer this, but I don't find it to be better than C based on my write up.
Answer choice E affirms the consequent.
In looking at my two choices, I'm going to have to dig deeper and actually diagram the conditional logic. I'll continue to use the numbers, but now I'm going to diagram 4 and 5 and see where it takes me.
4 = ~ 2 v ~ 3 --> ~ 1; 1 --> 2 ^ 3
5 = 2 ^ 3 --> 1; ~ 1 --> ~ 2 v ~ 3
In looking at number 5, there's a qualifier "quite probable" which means my initial analysis of D was unjust. I'm therefore going to have to add the qualifier into the equation:
2 ^ 3 --> probably 1; ~ 1 --> probably ~ 2 v ~ 3
Answer C is correct but is absolute. I'm now seeing that my initial reaction was incorrect because I omitted the qualifier in my initial write up.
Answer choice D is also correct, but includes the qualifier "likely" which is a synonym of "probably". You will see that this answer matches my updated contrapositive of #5 exactly.
Therefore, answer D.
I'm not sure if this helped or not, I wrote it out as I was going through it
You're right that the 4th statement contrasts with the 5th. It *almost* creates a biconditional, but it keeps the 2/3 lumped in such a way that it's not a true biconditional.