## What is the Contrapositive of this statement?

Prepare for the LSAT or discuss it with others in this forum.
rsuelzer

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

### What is the Contrapositive of this statement?

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?

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...

theZeigs

Posts: 148
Joined: Fri Nov 28, 2008 3:26 pm

### Re: What is the Contrapositive of this statement?

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

FreeGuy

Posts: 130
Joined: Sun Dec 21, 2008 4:42 pm

### Re: What is the Contrapositive of this statement?

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: 262
Joined: Sat Sep 19, 2009 2:53 am

### Re: What is the Contrapositive of this statement?

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.

hellojd

Posts: 412
Joined: Wed Jan 13, 2010 1:29 pm

### Re: What is the Contrapositive of this statement?

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.