Negating an unless statement

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suspicious android
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Re: Negating an unless statement

Postby suspicious android » Fri Aug 26, 2011 3:05 pm

lsatisevil wrote:The unless makes things really confusing. Just remember that when we come across it, the expression that it INTRODUCES is the necessary condition, and the sufficient condition is the negation of the remaining expression.


You're just quoting a way to diagram an unless statement. That is not at issue here.

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dakure
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Re: Negating an unless statement

Postby dakure » Fri Aug 26, 2011 3:20 pm

suspicious android wrote:
dakure wrote:The negation of an unless statement should not look like that. It should look like:
A-->B
A-->~B


To negate the sentence, you want to show the sufficient condition WITHOUT the necessary condition.


The first part of your post when you corrected the 'if not' thing is right on, and the people arguing for 'if not' being the negation of an 'unless' statement are just not understanding the point at issue.

However, you're not being completely consistent with your definition of a negated conditional. In the above quoted material you do two different things. The first is not precisely correct, although is often (usually?) a close enough approximation to get a correct answer on an LR question. The latter is perfect. To see the difference consider this conditional statement:

All the men here are Russian. (M --> R)

To negate this idea, you want simply to disagree with it in the safest way possible. To show it is false, you need only to provide an example of a single man here who is not Russian. So "Some men here are not Russian" or "M some ~R" if you go for that sort of diagramming method.

M --> ~R is inconsistent with the original statement but not quite the negation. EDIT: If you meant your first example just to be a quick and dirty polar opposite, I don't mean to correct you necessarily, but it's worthwhile to note the difference.

Bottom line: The proper negation of ANY conditional statement is never going to be another conditional statement.

I did, and I agree with you. I had a long diatribe earlier about how they will never be diagrammable statements. We're on the same page.

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suspicious android
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Re: Negating an unless statement

Postby suspicious android » Fri Aug 26, 2011 3:43 pm

dakure wrote:I did, and I agree with you. I had a long diatribe earlier about how they will never be diagrammable statements. We're on the same page.


Right on, there was so much noise and crosstalk I was confused about who was asserting what.

I've had this problem before with students confusing negation with contrapositives. It's always a really bad sign.

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Dave Hall
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Re: Negating an unless statement

Postby Dave Hall » Fri Aug 26, 2011 8:00 pm

6lehderjets wrote:Having a little trouble negating answer choices for assumption questions that have "unless" in them. How would negate the statement below?

People who attempt to jump of buildings are likely to do themselves more harm than good unless they have they something soft to land on...

Kind of a dark answer choice but the question stands! Thanks.


Take it in steps (our last step here will give us the only two steps you'll have to take in future. But first, I'll walk you all the way through the thinking):

1. Symbolize the conditional relationship (For a primer on a simple, mechanical way to symbolize "unless" statements, you can watch this free video lesson (LinkRemoved)).

2. You'll end up with this:

no Soft Landing --> Harm
no Harm --> Soft Landing

In other words, the meaning of your sentence is that a soft landing place is necessary to avoid doing "more harm than good" (which I've abbreviated here as "harm").

3. To negate any answer choice, you can always append the words "it's not true that..." to the front. Doing that, what we get in this instance is "It's not true that avoiding harm requires a soft landing".

4. We can reformulate that symbolically:

~ (no H --> SL)

5. So, your mechanical means of negating an unless-type statement boils down to two steps:

1. Formulate the choice symbolically.

2. Negate that symbol set.

Let's finish with another example:

You can't eat carrots unless you have teeth.

Step 1:

no T --> no C
C --> T

Step 2:

~ (C --> T)

And we end up with this: "It's not true that eating carrots requires teeth."

Hope that helps.

6lehderjets
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Re: Negating an unless statement

Postby 6lehderjets » Sat Aug 27, 2011 6:45 pm

Dave Hall wrote:
6lehderjets wrote:Having a little trouble negating answer choices for assumption questions that have "unless" in them. How would negate the statement below?

People who attempt to jump of buildings are likely to do themselves more harm than good unless they have they something soft to land on...

Kind of a dark answer choice but the question stands! Thanks.


Take it in steps (our last step here will give us the only two steps you'll have to take in future. But first, I'll walk you all the way through the thinking):

1. Symbolize the conditional relationship (For a primer on a simple, mechanical way to symbolize "unless" statements, you can watch this free video lesson (LinkRemoved)).

2. You'll end up with this:

no Soft Landing --> Harm
no Harm --> Soft Landing

In other words, the meaning of your sentence is that a soft landing place is necessary to avoid doing "more harm than good" (which I've abbreviated here as "harm").

3. To negate any answer choice, you can always append the words "it's not true that..." to the front. Doing that, what we get in this instance is "It's not true that avoiding harm requires a soft landing".

4. We can reformulate that symbolically:

~ (no H --> SL)

5. So, your mechanical means of negating an unless-type statement boils down to two steps:

1. Formulate the choice symbolically.

2. Negate that symbol set.

Let's finish with another example:

You can't eat carrots unless you have teeth.

Step 1:

no T --> no C
C --> T

Step 2:

~ (C --> T)

And we end up with this: "It's not true that eating carrots requires teeth."

Hope that helps.



Thanks Dave! Adding "its not true that" will definitely makes negating the particular answer choice I was reviewing easier.




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