Quantifiers Questions - - Question 16

No small countries and no countries in the southern hemisphere have permanent seats on the United Nations Security Co...

ajcaviness February 8, 2022

How she got to answer choice E

Hi, I understand all the diagramming and eliminating of answer choices up until E. I am confused on how she knew to use that particular quantifying rule right away and how she knew what principle to look at.

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Ravi February 9, 2022

In this argument, we have several statements:

1) small country or Southern Hemisphere-->no permanent seat

2) permanent seat-->increased peacekeeping and greater role

3) increased peacekeeping--some--against spending

There's not much to combine here, but we can combine the first two statements since they're both "all statements."

Taking the contrapositive of the first statement, we have

Permanent seat-->not small country and not Southern Hemisphere

Now this statement and statement two have their sufficient conditions in common, so we can combine them.

Permanent seat-->increased peacekeeping and greater role
Permanent seat-->not small country and not Southern Hemisphere

From this, we can conclude that

Not small country and not Southern Hemisphere--some--increased peacekeeping and greater role

Looking at E, this is a paraphrase of the deduction we came up with by combining the two "all" statements in the stimulus. Remember, if two "all" statements share a sufficient condition, then you can always make a "some" statement out of the necessary conditions from the two statements.

KiaBrodersen October 7, 2023

Hi Ravi,

I understand by your explanation and the reasoning of why you can combine two "all" or necessary and sufficient statements if they share the sufficient side in common. However, this was not in the lecture video as one of the rules. The first rule is that you must have a sufficient and necessary statement, and the one exception to this rule occurs when you have two "most" statements. I got this question incorrect because I didn't combine the two "all" statements into a "some" statement because I wasn't even aware that that was something to keep in mind. Just wanted to inform you all that you have blind spots in the lecture videos that, we, as your students, only learn upon getting an answer incorrect and then watching the question explanation video. Thank you.