Q13 - Nations that have little

[mshinners]

What does the Question Stem tell us?
Logical Completion (Inference … "It follows that ____")

Break down the Stimulus:
Read for Conditional, Causal, Comparative, Quantitative.
There are essentially three conditionals, and they chain together. Little interaction --> Little knowledge of needs/problems --> ~Sympathy and ~Justice

Any prephrase?
When conditionals chain together, the correct answer normally rewards us for finding the chain by testing the connection between the first part and the last part. So we might predict "If you have little interaction, you won't have sympathy or justice".

Answer choice analysis:
A) Illegal reversal.

B) Looks good.

C) "almost all" is too extreme. We can't support any quantifying of where problems come from.

D) "there is no way" is too extreme. Couldn't we help alleviate conflict by increasing the interaction nations have with each other?

E) This says "if you have knowledge, then you have interaction". It's pretty similar to the first sentence. However, the first sentence was comparative, not absolute. The rule provided was "if little interaction, then little knowledge". So we could contrapose that and get "if much knowledge, then much interaction". But E is speaking in absolute terms: whether or not there's interaction / whether or not there's knowledge. This answer choice also makes no use of the 2nd sentence. When a logical completion question is asking us to derive a conclusion, it's always asking us to pull together the two strands of thought into some synthesis. Since (E) only relates to the first sentence, it should be suspicious.

The correct answer is B.

Takeaway/Pattern: When we do logical completion (fill in the blank) and have to derive the author's conclusion, we're looking for a safe way of pulling together the various strands of thought. This question, like so many other Inference questions, provides multiple conditional ideas to see whether we can chain them together.

#officialexplanation

[atzhang6v6]

I have a quation about E...i thought if you make the logic contrapositive AND will become OR.
But in E its still sympathy AND justice after making the second sentence contrapositive.
Why is this allowed?

[ohthatpatrick]

Good question.

First of all, you know that the correct answer is B, right?

If we said
"Being in a good mood depends on getting enough sleep"
and
"Having energy all day long depends on getting enough sleep"

We could separately symbolize each of those as
Good mood --> enough sleep
and
All day energy --> enough sleep

I could be speaking about the important of good sleep and say something like,
"Both having a good mood and having energy throughout the day depend on getting enough sleep".

That wouldn't suddenly turn our conditionals into:
Good mood AND all day energy --> enough sleep

So I think you saw the conditional trigger "depend" and translated this sentence a little too literally into
X and Y --> Z

What it's trying to say is "X depends on Z and Y also depends on Z".

[huskybins]

Dear guru Patrick, I would still appreciate if you could offer your insightful opinion on why E is incorrect. Generally, I learnt from other places that a rule with "relative comparison" cannot be negated into a rule with "absolute" claim. Just like in this question, little interaction --> little knowledge; therefore, we should not take its contrapositive as knowledge --> interaction. But why? I would still appreciate if any example can be offered in explaining the above question.

Funny enough I checked other places one of which in video explains E as reversal logic, and some other simply mentions it as "silly".

Good question.

First of all, you know that the correct answer is B, right?

If we said
"Being in a good mood depends on getting enough sleep"
and
"Having energy all day long depends on getting enough sleep"

We could separately symbolize each of those as
Good mood --> enough sleep
and
All day energy --> enough sleep

I could be speaking about the important of good sleep and say something like,
"Both having a good mood and having energy throughout the day depend on getting enough sleep".

That wouldn't suddenly turn our conditionals into:
Good mood AND all day energy --> enough sleep

So I think you saw the conditional trigger "depend" and translated this sentence a little too literally into
X and Y --> Z

What it's trying to say is "X depends on Z and Y also depends on Z".

[ohthatpatrick]

Ha! Yeah, we've all had a moment of wanting to just call an answer choice "silly", without trying to articulate why it's wrong.

The first sentence, if we chose to diagram it, says
"If you have little interaction between two countries, you have little knowledge of each other's needs and problems".

The contrapositive would begin
IF IT IS NOT THE CASE THAT "you have little knowledge of each other's needs and problems", THEN ....

Well how do you understand / simplify the idea that "These two nations do NOT have little knowledge of each other's needs and problems"?

I would think of it as "These two nations have MUCH knowledge of each other's needs and problems".

Other people might think "These two nations have ZERO knowledge." To me, "ZERO knowledge" is still "little knowledge".

What does "little" mean?

We don't usually encounter it with any need for precision, but "little" seems to operate like "few".

Few NFL players are female. (true --- less than 50% of NFL players are female)
I have little interest in seeing that movie (I have no interest or barely any interest)

There's an annoying distinction here that if we say
"I have a little interest in seeing that movie", we ARE saying "I have at least some".
If we say
"I have little interest in seeing that movie", it's possible we're saying "I have none".

Similarly, saying
"A few NFL players are female" means that "there are at least some female NFL players"
whereas
"Few NFL players are female" can still mean "there are ZERO female NFL players".

So, to me, since "little" is compatible with "none", when we negate "little" we have to say "much / significant amount".

So the contrapositive of the 1st sentence is
"If two nations have MUCH knowledge of each other, then they have MUCH interaction."

(E) says
"If you have SOME knowledge, then you have SOME interaction."

Those are not the same rule.

People are probably saying (E) is silly because it's easy to have SOME knowledge of a nation's needs and problems without having any interaction.

Also, as we said in the explanation above, (E) is only dealing with the topic of the 1st sentence. Where are "sympathy" and "justice" in this answer choice? The author's conclusion (the ______ ) FOLLOWS from the fact that "sympathy and justice depend on understanding the needs and problems of others".

We can't pick an answer that in no way follows from / involves the concepts of "sympathy and justice".

[charlotte]

Hi Patrick,

I narrowed it down to A and B and picked A. I don't understand why A is illegal reversal. Could you explain, please?

[ohthatpatrick]

The first sentence says
"if you have little interaction ---> you'll have little knowledge of needs/problems"

The second sentence says
"sympathy ---requires----> understanding needs/problems"
and
"Justice ---requires----> understanding needs/problems"

So we could chain those together and get
if little interaction -> won't understand needs/problems -> No sympathy / justice

Regarding (A), we know that
If you DON'T have knowledge of needs/problems, you WON'T have symp/just

(A) says
If you DO have knowledge of needs/problems, you WILL have symp/just

This would be an illegal negation of what we know.