Can someone check if I am negating this correctly?

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stray
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Can someone check if I am negating this correctly?

Postby stray » Wed May 29, 2013 11:33 pm

Hey, so I am going through the Manhattan LSAT book and so far just the fundamentals, and there is a part on necessary and sufficient assumptions. Any who, I need to make sure I am doing this correctly.

If Maria attends church every Saturday, then she is a person who values faith.
Negation - If Maria does not attend church every Saturday, then she is not a person who values faith.
This one I am fairly certain about.

Anyone who attends church every Saturday is a person who values faith, family, and community.
Negation: Anyone who attends church Saturday IS NOT a person who values faith, family, and community.
Or would it be - Anyone who DOES NOT attend church Saturday IS NOT a person who values faith, family, and community.
Please explain.

Daily_Double
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Re: Can someone check if I am negating this correctly?

Postby Daily_Double » Wed May 29, 2013 11:41 pm

I think you're wrong, but I'm really tired so I'll just be brief. When you are negating a conditional statement, you're really saying, given some relationship, that when the sufficient condition occurs, it is not the case that the necessary condition occurs.

For example:

A ---> B

Negated, (it is not the case that when A happens, B happens)

A ---> ~ B

I will also say that I believe the negation test is overrated. I think after you drill hard, and just get used to spotting the gap in the argument, you don't need this. Wrong answers in N/A questions, for which the negation test is used, will be too strong, flawed (poor logic), or just outside the scope of the argument. You don't need the negation test to spot these.

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stray
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Re: Can someone check if I am negating this correctly?

Postby stray » Wed May 29, 2013 11:47 pm

Daily_Double wrote:I think you're wrong, but I'm really tired so I'll just be brief. When you are negating a conditional statement, you're really saying, given some relationship, that when the sufficient condition occurs, it is not the case that the necessary condition occurs.

For example:

A ---> B

Negated, (it is not the case that when A happens, B happens)

A ---> ~ B

I will also say that I believe the negation test is overrated. I think after you drill hard, and just get used to spotting the gap in the argument, you don't need this. Wrong answers in N/A questions, for which the negation test is used, will be too strong, flawed (poor logic), or just outside the scope of the argument. You don't need the negation test to spot these.


Yeah you are probably correct in saying that I eventually wont need it by the time I get through this entire book and do a shitload of questions, but I just kinda wanted to go through the book first and fully understand it. Can someone else check my negations?

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suralin
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Re: Can someone check if I am negating this correctly?

Postby suralin » Thu May 30, 2013 12:07 am

ColumbiaBigLaw wrote:
Daily_Double wrote:I think you're wrong, but I'm really tired so I'll just be brief. When you are negating a conditional statement, you're really saying, given some relationship, that when the sufficient condition occurs, it is not the case that the necessary condition occurs.

For example:

A ---> B

Negated, (it is not the case that when A happens, B happens)

A ---> ~ B

I will also say that I believe the negation test is overrated. I think after you drill hard, and just get used to spotting the gap in the argument, you don't need this. Wrong answers in N/A questions, for which the negation test is used, will be too strong, flawed (poor logic), or just outside the scope of the argument. You don't need the negation test to spot these.


Yeah you are probably correct in saying that I eventually wont need it by the time I get through this entire book and do a shitload of questions, but I just kinda wanted to go through the book first and fully understand it. Can someone else check my negations?


Haven't started seriously prepping for the LSAT, but this past semester I took two courses dealing with formal logic so hopefully I can help.

The other poster is correct. Think of it this way: if I say, "If the sky is blue, then I am on TLS," I am essentially stating a hypothesis. How would somebody verify my hypothesis? Well, the only way to disprove my hypothesis would be for it to simultaneously be the case that the sky is blue but not the case that I am on TLS. In other words, the truth of the proposition "the sky is blue" is sufficient for the proposition "I am on TLS" to be true, and thus if "the sky is blue" is true and "I am on TLS" is untrue, then "the sky is blue" is not in fact sufficient: the conditional has been negated. You can check this by doing a truth table (you can just look this up); the conditional A --> B (if A, then B) is false if and only if A is true and B is false. (In all other cases, the conditional would be true.)

Your first example is actually the inverse fallacy (negating both the antecedent and the consequent), not the negation of the conditional.
In your second example, the first negation is correct.

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stray
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Re: Can someone check if I am negating this correctly?

Postby stray » Thu May 30, 2013 12:23 am

I thank you both for the help! Good luck guys.

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Hspeaksfriend
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Re: Can someone check if I am negating this correctly?

Postby Hspeaksfriend » Thu May 30, 2013 12:35 am

ColumbiaBigLaw wrote:Hey, so I am going through the Manhattan LSAT book and so far just the fundamentals, and there is a part on necessary and sufficient assumptions. Any who, I need to make sure I am doing this correctly.

If Maria attends church every Saturday, then she is a person who values faith.
Negation - If Maria does not attend church every Saturday, then she is not a person who values faith.
This one I am fairly certain about.

Anyone who attends church every Saturday is a person who values faith, family, and community.
Negation: Anyone who attends church Saturday IS NOT a person who values faith, family, and community.
Or would it be - Anyone who DOES NOT attend church Saturday IS NOT a person who values faith, family, and community.
Please explain.


Correct way to negate the first example is this:
Even if Maria attends church every Saturday, she might not be a person who values faith.

Correct way to negate the second example is this:
Anyone who attends church every Saturday might not be a person who values faith, family, and community.

kaiser
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Re: Can someone check if I am negating this correctly?

Postby kaiser » Thu May 30, 2013 12:50 am

Hspeaksfriend wrote:
ColumbiaBigLaw wrote:Hey, so I am going through the Manhattan LSAT book and so far just the fundamentals, and there is a part on necessary and sufficient assumptions. Any who, I need to make sure I am doing this correctly.

If Maria attends church every Saturday, then she is a person who values faith.
Negation - If Maria does not attend church every Saturday, then she is not a person who values faith.
This one I am fairly certain about.

Anyone who attends church every Saturday is a person who values faith, family, and community.
Negation: Anyone who attends church Saturday IS NOT a person who values faith, family, and community.
Or would it be - Anyone who DOES NOT attend church Saturday IS NOT a person who values faith, family, and community.
Please explain.


Correct way to negate the first example is this:
Even if Maria attends church every Saturday, she might not be a person who values faith.

Correct way to negate the second example is this:
Anyone who attends church every Saturday might not be a person who values faith, family, and community.


This post is not correct. Here are the proper negations. I'll reduce them to short forms & symbols to make it more clear.

First one says, if she goes to church every Sunday, then she values faith. So, if church every saturday (CS), then values faith (VF):

CS --> VF

When you negate a conditional statement (i.e. reach the contrapositive), you first negate the necessary condition. Once you negate the necessary condition, you have deductively precluded the occurrence of the sufficient condition:

NOT VF --> NOT CS

Put back into real terms, this means that, if Maria is NOT someone who values faith, she will NOT attend church every Saturday (since valuation of faith is a necessary prerequisite among those who attend church every Saturday, pursuant to the original conditional statement).

Now lets do the 2nd one. First, lets reduce it to necessary & sufficient language. Of course, keep in mind what a sufficient condition actually is. Its essentially a statement about EVERY member of a group (as defined by whatever the sufficient condition is). What do we know about each member of that group? We know that some necessary condition is deductively associated with their inclusion in the group.

So lets take the statement here. Anyone who attends church on Saturday is a person who values faith, family and community. So we know something about an entire class of people (those who go to church on Sat). What do we know? That every single one values faith, family and community (i.e. they value all 3 of these things combined). If an individual is lacking in any of these values (i.e. does NOT value faith, family, OR community, or some combination), then that person CANNOT be someone who attends church every Saturday. Because, if he did attend church every Sat., then he WOULD value them all. Even if the person values 2 of those things, that isn't enough. Unless he/she values all 3, he is not someone who attends church on Sat.

Church Sat --> Values F, F, and C

Does NOT value F, F, OR C --> does NOT attend church Sat.

So, the negation of the second one is as follows: "Anyone who does NOT value faith, family, OR community does NOT attend church each Sat".

Just be clear with the "and" to "or" in the negation and you are fine.

Sorry for the length of the post, but I wanted to make this immensely clear for you.

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Hspeaksfriend
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Re: Can someone check if I am negating this correctly?

Postby Hspeaksfriend » Thu May 30, 2013 12:54 am

kaiser wrote:
Hspeaksfriend wrote:
ColumbiaBigLaw wrote:Hey, so I am going through the Manhattan LSAT book and so far just the fundamentals, and there is a part on necessary and sufficient assumptions. Any who, I need to make sure I am doing this correctly.

If Maria attends church every Saturday, then she is a person who values faith.
Negation - If Maria does not attend church every Saturday, then she is not a person who values faith.
This one I am fairly certain about.

Anyone who attends church every Saturday is a person who values faith, family, and community.
Negation: Anyone who attends church Saturday IS NOT a person who values faith, family, and community.
Or would it be - Anyone who DOES NOT attend church Saturday IS NOT a person who values faith, family, and community.
Please explain.


Correct way to negate the first example is this:
Even if Maria attends church every Saturday, she might not be a person who values faith.

Correct way to negate the second example is this:
Anyone who attends church every Saturday might not be a person who values faith, family, and community.


This post is not correct. Here are the proper negations. I'll reduce them to short forms & symbols to make it more clear.

First one says, if she goes to church every Sunday, then she values faith. So, if church every sunday (CS), then values faith (VF):

CS --> VF

When you negate a conditional statement (i.e. reach the contrapositive), you first negate the necessary condition. Once you negate the necessary condition, you have deductively precluded the occurrence of the sufficient condition:

NOT VF --> NOT CS

Put back into real terms, this means that, if Maria is NOT someone who values faith, she will NOT attend church every Sunday (since valuation of faith is a necessary prerequisite among those who attend church every Sunday, pursuant to the original conditional statement).

Now lets do the 2nd one. First, lets reduce it to necessary & sufficient language. Of course, keep in mind what a sufficient condition actually is. Its essentially a statement about EVERY member of a group (as defined by whatever the sufficient condition is). What do we know about each member of that group? We know that some necessary condition is deductively associated with their inclusion in the group.

So lets take the statement here. Anyone who attends church on Saturday is a person who values faith, family and community. So we know something about an entire class of people (those who go to church on Sat). What do we know? That every single one values faith, family and community (i.e. they value all 3 of these things combined). If an individual is lacking in any of these values (i.e. does NOT value faith, family, OR community, or some combination), then that person CANNOT be someone who attends church every Saturday. Because, if he did attend church every Sat., then he WOULD value them all. Even if the person values 2 of those things, that isn't enough. Unless he/she values all 3, he is not someone who attends church on Sat.

Church Sat --> Values F, F, and C

Does NOT value F, F, OR C --> does NOT attend church Sat.

So, the negation of the second one is as follows: "Anyone who does NOT value faith, family, OR community does NOT attend church each Sat".

Just be clear with the "and" to "or" in the negation and you are fine.

Sorry for the length of the post, but I wanted to make this immensely clear for you.


This is not correct either. What you did was take the contrapositive which is COMPLETELY different than negating a statement FYI

OP, I'm an LSAT instructor. If I were you, I would stick with my response.

EDIT: OP, are you trying to negate these statements or take the contrapositive? If you're trying to negate them, then my response is correct. If you're trying to take the contrapositive, then kaiser is right.

kaiser
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Re: Can someone check if I am negating this correctly?

Postby kaiser » Thu May 30, 2013 1:03 am

^^

Gotcha. I assumed from the get go that OP was simply asking how to find the contrapositive. Perhaps my reading comprehension needs a tune up. Well, at least OP now knows precisely what to do regardless of what he is trying to do with the statements.

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suralin
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Re: Can someone check if I am negating this correctly?

Postby suralin » Thu May 30, 2013 1:05 am

kaiser wrote:
Hspeaksfriend wrote:
ColumbiaBigLaw wrote:Hey, so I am going through the Manhattan LSAT book and so far just the fundamentals, and there is a part on necessary and sufficient assumptions. Any who, I need to make sure I am doing this correctly.

If Maria attends church every Saturday, then she is a person who values faith.
Negation - If Maria does not attend church every Saturday, then she is not a person who values faith.
This one I am fairly certain about.

Anyone who attends church every Saturday is a person who values faith, family, and community.
Negation: Anyone who attends church Saturday IS NOT a person who values faith, family, and community.
Or would it be - Anyone who DOES NOT attend church Saturday IS NOT a person who values faith, family, and community.
Please explain.


Correct way to negate the first example is this:
Even if Maria attends church every Saturday, she might not be a person who values faith.

Correct way to negate the second example is this:
Anyone who attends church every Saturday might not be a person who values faith, family, and community.


This post is not correct. Here are the proper negations. I'll reduce them to short forms & symbols to make it more clear.

First one says, if she goes to church every Sunday, then she values faith. So, if church every saturday (CS), then values faith (VF):

CS --> VF

When you negate a conditional statement (i.e. reach the contrapositive), you first negate the necessary condition. Once you negate the necessary condition, you have deductively precluded the occurrence of the sufficient condition:

NOT VF --> NOT CS

Put back into real terms, this means that, if Maria is NOT someone who values faith, she will NOT attend church every Saturday (since valuation of faith is a necessary prerequisite among those who attend church every Saturday, pursuant to the original conditional statement).

Now lets do the 2nd one. First, lets reduce it to necessary & sufficient language. Of course, keep in mind what a sufficient condition actually is. Its essentially a statement about EVERY member of a group (as defined by whatever the sufficient condition is). What do we know about each member of that group? We know that some necessary condition is deductively associated with their inclusion in the group.

So lets take the statement here. Anyone who attends church on Saturday is a person who values faith, family and community. So we know something about an entire class of people (those who go to church on Sat). What do we know? That every single one values faith, family and community (i.e. they value all 3 of these things combined). If an individual is lacking in any of these values (i.e. does NOT value faith, family, OR community, or some combination), then that person CANNOT be someone who attends church every Saturday. Because, if he did attend church every Sat., then he WOULD value them all. Even if the person values 2 of those things, that isn't enough. Unless he/she values all 3, he is not someone who attends church on Sat.

Church Sat --> Values F, F, and C

Does NOT value F, F, OR C --> does NOT attend church Sat.

So, the negation of the second one is as follows: "Anyone who does NOT value faith, family, OR community does NOT attend church each Sat".

Just be clear with the "and" to "or" in the negation and you are fine.

Sorry for the length of the post, but I wanted to make this immensely clear for you.


This is just wrong. The contrapositive of a conditional C is logically equivalent to C, not the negation of C.

The negation of a conditional is the conjunction of the antecedent and the negated consequent, as follows:
~(p → q) ≡ p ∧ ~q

See, e.g., http://www.personal.kent.edu/~rmuhamma/ ... tional.htm and http://www.regentsprep.org/Regents/math ... mpound.htm.

Edit: Okay, I see now that it was a RC mix-up. Good information ITT regardless.

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stray
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Re: Can someone check if I am negating this correctly?

Postby stray » Thu May 30, 2013 10:23 am

I was trying to just negate them, not get the contrapositive, but thanks anyways Kaiser - actually what confused me before was I think I was trying to negate in the manner you would if you were trying to get the contrapositive. So your post actually helped me realize that these are strictly two different "negations". Thanks again guys.

Just to be clear, is this correct? - To get a contrapositive, you would take "If A, then B" and negate and reverse to make it "If NOT B, then NOT A"
Just for a simple negation for necessary assumption equations, you take "If A, then B" and make it "If A, then Not B".

bp shinners
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Re: Can someone check if I am negating this correctly?

Postby bp shinners » Thu May 30, 2013 12:38 pm

ColumbiaBigLaw wrote:Just to be clear, is this correct? - To get a contrapositive, you would take "If A, then B" and negate and reverse to make it "If NOT B, then NOT A"


Correct.

Just for a simple negation for necessary assumption equations, you take "If A, then B" and make it "If A, then Not B".


Incorrect. To negate a conditional, you say that you can have the sufficient condition without necessarily having the necessary condition. You might still have it, but you also might not. Essentially, the negation is that A is not longer sufficient to tell you B.

So the negation of "If A, then B" is "If A, maybe or maybe not B." Or, in better language, "A doesn't guarantee B", "Even if A, not sure of B", etc...

rambleon65
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Re: Can someone check if I am negating this correctly?

Postby rambleon65 » Fri May 31, 2013 3:02 am

Didn't read everybody's response, but essentially, negation should prove that the rule doesn't always kick.
Meaning, the negation should state A does not necessarily mean B.

Which, importantly, is different from A -> ~B.
A could still mean B, but not necessarily. This "not-necessarily" is sufficient to negate A->B.

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suralin
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Re: Can someone check if I am negating this correctly?

Postby suralin » Fri May 31, 2013 3:48 pm

rambleon65 wrote:Didn't read everybody's response, but essentially, negation should prove that the rule doesn't always kick.
Meaning, the negation should state A does not necessarily mean B.

Which, importantly, is different from A -> ~B.
A could still mean B, but not necessarily. This "not-necessarily" is sufficient to negate A->B.


Yeah, ~(A → B) ≡ A ^ ~B, but A ^ ~B !≡ A → ~B.

That falls out from this:

A → B ≡ ~A ∨ B [ easily seen from consideration or just from a truth table ]
~(A → B) ≡ ~(~A ∨ B) [ negate both sides ]
~(A → B) ≡ A ^ ~ B [ by De Morgan's laws ]

And ~(A → B) !≡ A → ~B [ intuitive/from a truth table ]
so A ^ ~B !≡ A → ~B.

All of this stuff is derivable or shown from a truth table, so if you really want to make sure you understand it, just prove it.




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