What is the Contrapositive of this statement? Forum

[rsuelzer]

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]

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]

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]

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]

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]

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.