Negating Some and all LR Ch3-P61, Q2 and Q7

[MonaA136]

Hello,

I have a couple of questions regarding negating some and all.

Logical reasoning Manhattan Prep book, P.61, Q2 and Q7.

Q2. All of us are with you.
Negating:
Not all of us with you.--> Agree
Some of us are Not with you. --> shouldn't this be "some of us ARE with you"? why the verb is also negated?
Is this because of the followings:
we can infer from "All of us with you" that Some of us are with you" and then we negate the verb. what is the process here.

Q7. None of the actors are in the union.
Some of the actors are in the union.--> Agree
Not all of the actors are OUT of the Union--> could I get more explanation on this one too.

I thought that the process of negating is as follows:
Find the modifier and negate the modifier.
if there is no modifier, negate the verb.

Thank you very much

[ohthatpatrick]

Yeah, you're right about the rules of negating.

1. If the truth value hinges on a quantifier, contradict the quantifier.

2. If the truth value hinges on a verb, contradict the verb.

3. If the truth value hinges on a "not", contradict the "not".

4. If the answer choice uses conditional language, don't try negating it. (People always mess it up, and it's not super helpful)
Instead, just ask whether author made that same move in the argument. Make sure the order of ideas is correct (no reversals or negations of the argument core) and make sure that the author's move was so SURE of itself that we can fairly accuse him of assuming a black-and-white conditional.




Some of us are Not with you.

This hinges on quantity. It says "AT LEAST ONE of us is not with you."
When we negate "some", we always get "none".
Some = AT LEAST ONE
so, to contradict AT LEAST ONE you have to say ZERO.


So, the negation is
NONE of us are not with you.

That's a double negative, so if you want to clean it up and state it positively, you say
All of us are WITH you.

-------
Be careful, because you were thinking that negating "Some A's are B" is "Some A's are not B".

If I say "Some lawyers are Democrats" and "Some lawyers are not Democrats", have I contradicted myself?
No, those are compatible statements.

Negating = contradicting (in the most minimal fashion)
-------


Not all of the actors are OUT of the Union


The truth value of this claim hinges on quantity (or on the word 'not' ... take your pick).
Either "ALL the actors are out" or "NOT ALL the actors are out".

Every time we negate "not all" we get "all".

NEGATION: All of the actors are out of the Union.

If you wanted to rephrase that as "None of the actors are in the Union" you could, but there's no real reason to do (as there was when we wanted to better compute a double negative in the earlier example).

Hope this helps.