Negate conditional lawgic

emli1000

Question:

What is the difference between
A-->B
______
A-->/C

and

A--->B
_____
not (A--->C)

blah170blah

They have an inverse relationship, meaning that no valid inference can be made about the two (/A --> C is the inverse of A--> /C)

emli1000

I still don't understand

brna0714

Here is what I understand about the two, take it for what it's worth. A-->/C tells us that every single A is "not C" and it also tells us via the contrapositive that C-->/A, every single C is "not A." The other statement, not (A-->C), simply translates into "it is not that case that all A's are C's." That could mean anything from 99 out of 100 A's are C's (and one A is not) to absolutely no A's are C's. In other words, A-->C negates to A some /C (some A's exist that are not C's.) I hope that helps. If anyone discovers an error, please feel free to correct.

Alex Short

If you have to negate a conditional statement, just show that the necessary condition does not have to occur in order for the sufficient condition to occur.

I'm not sure what question you're looking at, but usually avoiding any unnecessary diagramming and focusing instead on the argument and personalizing it helps. Then, once the conditional relationship is clear for you, and if your objective requires you to negate it, look for an answer choice that establishes the sufficient condition occurring and the necessary condition not occurring at the same time.

emli1000

@brna0714 Thank you. That's the way of reasoning behind it in my head but for some reason when I see it in an answer choice I'm always stuck between two answer choices. I think I may have to revisit the lessons on that.

emli1000

@"Alex Short" Thanks, I'm going to review the lessons on SC & NC.

bobalicious

I agree with @brna0714

(1) All Apples are not Carrots
v.
(2) Not (all Apples are Carrots) = Some Apples are not Carrots. Note that that statement allows for the possibility of something being an Apple AND a Carrot. That's something sentence (1) does NOT allow.

emli1000

@bobalicious Thank you.