HW Question LR Book

[AlexY297]

Hello, I was wondering about the Some and Most part of conditional logic on the Logical Reasoning Book p. 374.

1.Some cars are sedans and some cars are red.
A)Most cars are sedans are red.
B)Some things that are red are cars.
C)None of the above.

3.Most children play sports and some children play instruments.
A)Some children who play instruments play sports.
B)Some people who plays sports are children.
C)None of the above.

Now I thought regarding Some + Some and Most + Some statements, we can't infer anything about the overlap. There may or may not be one but according to the solution for #1 it is B and for #3 it is B too. Can someone explain this a little further please? Thank you, Alex

[ohthatpatrick]

You're correct Alex. You wouldn't be able to make any OVERLAP inferences (i.e. you wouldn't be able to prove that the other qualities have to overlap).

But neither of the correct answers are doing that. They're not combining two facts to derive an inference. They're only deriving an inference from one of the facts.

1.Some cars are sedans and some cars are red.
A)Most cars are sedans are red.
B)Some things that are red are cars.
C)None of the above.

3.Most children play sports and some children play instruments.
A)Some children who play instruments play sports.
B)Some people who plays sports are children.
C)None of the above.


In the first example, cars is the overlapping ingredient in each statement. Do we combine the other qualities? Do we say that "sedan and red" have to overlap?

No, we're just saying "if at least one car is red", then "at least one red thing is a car". Some statements are reversible.

In the second example, children are the overlapping ingredient, and there's no way to prove that "sports and instruments" have to overlap. But the correct answer is just saying "if more than 50% of children play sports", then "at least one person who plays sports is a child".

Make sense?

[AlexY297]

Oh I see what you mean. In each example, it is asking you what is something shared by both or what is provable? Am I wording it properly?

[ohthatpatrick]

The instructions just say "choose which answer must be true".

With some of the examples, it must be true that there is some overlap.
With other examples, it doesn't have to be true that there is an overlap. But they can still just offer you a different true-idea that's based off of only one claim.

For Q3, for example, if we know that "Most children play sports"
then it must be true that

B)Some people who plays sports are children. (at least one person who plays sports is a child)

[AlexY297]

Hi I have a question about Negate This Drill:

-Silicon chips are a trait found in the central processor of all consumer computers.

Answer: Some consumer computers do not include silicon chips in their central processor.

I would have written: "Silicon chips are not a trait found in the central processor of all consumer computers."

So in these negation drills "all" becomes some or not all. I guess I just thought it would been a little different wording: "Silicon chips are not found in some consumer computers."

Am I looking at this too much ?

Thank you,
Alex

[AlexY297]

Another Negate This problem:

Example 1:
"Aggressive questioning should be allowed only if the witness is likely to provide useful information."

-"Aggressive questioning should be allowed at least sometimes even if the witness is NOT likely to provide useful information."

Seeing the transition of this negation with NOT and AT LEAST SOMETIMES, how do you know when to apply two negation changes to a sentence? Also changing the ONLY IF into EVEN IF... possible typo?


Example 2:
"The value of treating witnesses w/respect is outweighed in at least some cases by the need to extract information as soon as possible."

-"The value of treating witnesses w/respect is NEVER outweighed by the need to extract information as soon as possible."

So for this cases, IS changed into NEVER and AT LEAST SOME changed to none. Thus, the sentence has NEVER and a NONE making into "is never outweighed by the need to extract information as soon as possible" to make grammatical sense? I wanted to check my thought process here.

Thank you,
Alex

[ohthatpatrick]

For the silicon chips example,
-Silicon chips are a trait found in the central processor of all consumer computers.

your negation was totally correct. It's equivalent in meaning to the one the book provided. There's no one correct way to word it, as long as you have the right meaning.

In general, when we see "not all" on the test, it's a good habit to rephrase it as "some aren't".
If I hear "Not all tomatoes have seeds", I think "at least one tomato doesn't have seeds".


Example 2:
"The value of treating witnesses w/respect is outweighed in at least some cases by the need to extract information as soon as possible."

-"The value of treating witnesses w/respect is NEVER outweighed by the need to extract information as soon as possible."

So for this cases, IS changed into NEVER and AT LEAST SOME changed to none. Thus, the sentence has NEVER and a NONE making into "is never outweighed by the need to extract information as soon as possible" to make grammatical sense? I wanted to check my thought process here.

If you're contradicting "in at least some cases", you have to be saying "in ZERO cases". I don't know why you're saying "IS changed to NEVER". The word "is" appears in both sentences. They just switched from "at least some (one) cases" to "zero cases".


For this Example 1:
"Aggressive questioning should be allowed only if the witness is likely to provide useful information."

-"Aggressive questioning should be allowed at least sometimes even if the witness is NOT likely to provide useful information."

Seeing the transition of this negation with NOT and AT LEAST SOMETIMES, how do you know when to apply two negation changes to a sentence? Also changing the ONLY IF into EVEN IF... possible typo?

All negations are the same: you contradict the statement in the most minimal fashion possible. I hate the way the book writes this contradiction, but it's conveying a contradiction.

#1. Don't negate conditionals.
Students always mess it up, and it's not helpful to your analysis. If you see a conditional answer on Necessary Assumption, it's usually too strong to be correct. Ask yourself if it matches a reasoning move the author made, but expect that the vast majority of these will be illegal reversals or negations. If the author made a certain move from Idea X to Idea Y, then it's fine to say he's assuming that "If X, then Y". In all other cases, you would reject a conditional answer choice.

#2. If you're actually trying to contradict or negate a conditional (same thing), you don't get a conditional.
Contradicting a conditional is just saying "there's at least one counterexample".

GIVEN: If you're a girl, you love ballet.
CONTRADICTION: At least one girl doesn't love ballet.

Or in the annoying formulation of the book,
You might not love ballet even if you're a girl. (ugh, so bad)

Contradicting a conditional (if X, then Y) will always take this form:
it's possible that something is X but not Y.


Hope this helps.