What is the Contrapositive of this statement?

rsuelzer
Posts: 22
Joined: Tue Apr 13, 2010 5:10 am

What is the Contrapositive of this statement?

Postby rsuelzer » Wed Apr 21, 2010 4:30 am

If N is reduced, neither R nor S is reduced.

I am reading this right that

If N is reduced then R and S are not reduced.

Which would mean that the counter positive is:

If R or S is reduced then N is not reduced.


Apparently this is wrong. How do I interpret Neither, Nor statements?

rsuelzer
Posts: 22
Joined: Tue Apr 13, 2010 5:10 am

Re: What is the Contrapositive of this statement?

Postby rsuelzer » Wed Apr 21, 2010 4:32 am

Nevermind, I read the question wrong. But I still want to know if I am reading that statement correctly.

Funny how "not" in a question totally changes the answer...

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theZeigs
Posts: 138
Joined: Fri Nov 28, 2008 3:26 pm

Re: What is the Contrapositive of this statement?

Postby theZeigs » Wed Apr 21, 2010 9:50 am

That is correct. Diagrammed

N --> -R AND -S
equivalent:
N --> -(R AND S)

contrapostive:

R or S --> -N
equivalent
R or S (or both) --> -N

Well done sir

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FreeGuy
Posts: 133
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Re: What is the Contrapositive of this statement?

Postby FreeGuy » Wed Apr 21, 2010 10:04 am

Think of the rule as two separate statements and it's much easier to manage

N --> ~R
N --> ~S


contrapositives:

R --> ~N
S --> ~N

skip james
Posts: 264
Joined: Sat Sep 19, 2009 2:53 am

Re: What is the Contrapositive of this statement?

Postby skip james » Thu Apr 22, 2010 12:27 pm

FreeGuy wrote:Think of the rule as two separate statements and it's much easier to manage

N --> ~R
N --> ~S


contrapositives:

R --> ~N
S --> ~N


yeah this is the way to go about it.

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hellojd
Posts: 411
Joined: Wed Jan 13, 2010 1:29 pm

Re: What is the Contrapositive of this statement?

Postby hellojd » Thu Apr 22, 2010 4:31 pm

skip james wrote:
FreeGuy wrote:Think of the rule as two separate statements and it's much easier to manage

N --> ~R
N --> ~S


contrapositives:

R --> ~N
S --> ~N


yeah this is the way to go about it.

+1

Even though in the LRB it says to do it in one statement, if x ---> y and z, it's usually easier to split into z ---> y and x---> z. x ---> y or z is best left as one statement obviously.




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