Need your help

Let's diagram: "No economic system that is centrally planned can efficiently allocate resources" P1: ESCP ==> not EAR EAR ==> not ESCP "efficient allocation of resources is a necessary condition for achieving a national debt of less than 5% of GDP" P2: NDL5% ==> EAR not EAR ==> not NDL5% "It follows that any nation with a centrally planned economy has a national debt that is at least 5% of GDP" C: ESCP ==> not NDL5% NDL5% ==> not ESCP We connect the general rule of the first principle to the contrapositive of the second principle: ESCP ==> not EAR ==> not NDL5% to conclude: ESCP ==> not NDL5%. This is a valid transitive argument. Let's diagram (B): "such problems occur only where there is a large concentration of automobiles" P1: MAP ==> LCA not LCA ==> not MAP "there are no such places in the rural districts" P2: RD ==> not LCA LCA ==> not RD "All of the rural districts are free of major air pollution problems" C: RD ==> not MAP MAP ==> not RD Here, as we did in the argument, we take the general rule of one of the principles and connect it to the contrapositive of the remaining principle: RD ==> not LCA ==> not MAP to conclude: RD ==> not MAP. Thus, we have similar reasoning to the stimulus. Hope that helped! Let us know if you have any other questions!

Thanks a lot!!!

Hello. I don't necessarily need help with the question but I don't know how to diagram NOT All statements like answer choice A. Can you please show me how. Thank you!

No problem! So let's look at the basic rule: Not all A's are B's. What does "not all" mean? It means that we do not have 100%. So, since this could be anything from 1 out of 100 or 99 out of 100, we consider this a "some" so that we can encompass all options. So, we can rewrite this: Some A's are not B's. We then diagram this as: A-some-not B Answer choice (A) states: "Not all mammals are without wings," So, that means some mammals have wings, like the example it gives us: bats. We diagram this: M-some-W W-some-M Hope that helps! Please let us know if you have any other questions.

Does choice D not work because it's not invoking the contrapositive?

Hi @Glee, thanks for your post. As explained earlier on this thread, the reasoning in the stimulus and the correct answer choice involves valid transitive statements, some of which involve contrapositives. By contrast, in answer choice (D), there is no contrapositive or valid transitive argument. The statement "this implies that receiving large regular royalties is a necessary condition of being a famous rock star" is NOT AT ALL supported by the sufficient and necessary statements that precede it. So (D) must be eliminated. Hope that helps, please let us know if you have any additional questions.