Where is the lesson on negating embedded conditional statements?

miguel6zavala

I just need some clarification now how NOT (A--->B) turns into A and /B.

miguel6zavala

In (A--->B) ---> C. Couldn't the contrapositive just be
/C---> A--->/B. I am not getting how it gets to /C---> A and /B.

miguel6zavala

So if I had this statement: No candy is bitter. NO(C-->B) meaning C-->/B could that translate to C and /B. You can have candy and it not be bitter. Is that right? I think I am over thinking it a lot...

David Wayne

NOT (A->B) simply means that this conditional relationship is not true of our world. The way in which this is expressed is that A occurs without B occurring. So we'd need to go out in our world and observe A and /B. That proves that A does not lead to B. So A and /B occurring proves NOT (A->B).

No candy is bitter is a regular conditional statement. If i have a candy, i know it isn't bitter.

C->/B.

Concurrently, the contrapositive expresses the idea that if i have something bitter, i know it cannot be candy:

B->/C.

(A--->B) ---> C means that if the conditional relationship of A->B is true, than C occurs. If C fails to occur, then we know that the conditional relationship of A->B is not true. Be careful here though; that doesn't means A and /B both MUST occur. It just means that A doesn't necessarily lead to B. It means that i need to be able to have A and /B occur concurrently.

JY explains this all in Preptest 42 Section 2 Question 19.

vandyzach

Miguel, you are on the right track, but your last post seems to suggest that you're translating English into conditional logic incorrectly.

Christian Wayne explains the contrapositive perfectly. Just to clean it up into a few lines:

"No candy is bitter".

Candy ----> NOT Bitter

The contrapositive is: Bitter ----> NOT candy.

So if a substance is bitter, you know that it cannot possibly be candy.

Now, for the part of your post that I'm really concerned about:

NO, you CANNOT have a candy that is bitter, because of the definition of necessity. If the sufficient condition is met, the necessary will ALWAYS follow. Conditional arrows don't mess around.

Do you see what I mean? Please follow up! You are right on the brink of understanding a huge concept that the LSAT tests.