How to negate conditional statement

oceanlee14

Isn’t negating A=>B equals to A=>not B? If Luke goes to party, I will go as well. How to negate this conditional statement?

AngusMcGillis

Hey A -> B negated is (some A are not B ), it shows that all A are B, isn't in fact true

"“All Jedi use the Force.”

Did you say “No Jedi use the Force?” That’s not right. To negate this statement, you’re denying the conditional relationship between the categories Jedi and Force users. Whereas the original statement is stipulating that the categories of J and F exist in a conditional relationship, you’re saying J is not sufficient for F (and F is not necessary for J). So, in English, it becomes an intersection statement.

“Some Jedi do not use the Force.”"
https://7sage.com/negate-statements-lsat/

BinghamtonDave

The short answer is: Luke goes to the party and I won't

The longer answer attempts to get a grasp on what is going on when we negate a conditional statement. If I say: A---->B, I am saying that A and B exist in a relationship. That if A occurs then B occurs. Put differently, B occurring is necessary for the occurrence of A.
So if something is cat, then it is mammal. Being a mammal is necessary for something being a cat.
Cat---->mammal
When we deny a conditional relationship, we are denying that those two things exist in a sufficient/necessary relationship. Operationally, what we do is keep the sufficient condition, replace the arrow with an "and" and negate the necessary condition.

Now, what does it mean to negate the conditional relationship? When we negate:
Cat--->Mammal
to become
Cat and Mammal
we are in effect saying that the conditional relationship:
Cat--->Mammal does not exist
Because if that conditional relationship did exist, when we didn't have a mammal, we wouldn't have a cat! But the existence of a mammal and a cat tells us that those two elements do not exist in the relationship:
Cat---->mammal

I hope this helps!
David