Need help with "ALL"

Lsatbreakingnews

I'm confused because I am in the some and most relationships lessons and the word "ALL" is being brought back from conditional logic. From my understanding "All" is a group 1 sufficient condition indicator in conditional logic. So for example All J are F = (J --> F) and to negate we take the contrapositive (/F --> /J) however in the some and most relationships lessons were being told to take "ALL" and negate it using "some not" which would bring (J --> F) into ( J some /F). So whats the difference between the two, when should we use one over the other I'm just kind of confused.

quinnxzhang

@Euthyphro said:
So for example All J are F = (J --> F) and to negate we take the contrapositive (/F --> /J)

The negation of 'J → F' is not '/F → /J'. The contrapositive is logically equivalent to the conditional, so it can't be the conditional's negation. That is, the negation of P is true when P is false and is false when P is true. However, '/F → /J' is true when 'J → F' is true and false when 'J → F' is false.

That said, there are still lots of problems with the way LSAT courses translate quantified sentences. In no logic course would "all J are F" be translated into 'J → F', and I think it hurts students to do this. However, for the sake of this curriculum, you're probably better off just memorizing that the negation of "all" is "some not".

Lsatbreakingnews

Ah I see. So contrapositive is not a negation just the same logically equivalent statement. Thanks I will just memorize that All's negation as "Some Not". Thanks again