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embedded conditionals

alexroark5alexroark5 Alum Member Inactive ⭐
in General 812 karma
Ok question on this. Lets say we have "if A then no B unless C". According to JY we can diagram as follows:

A-->(B-->C)
we pull the first term in the parentheses out and make the arrow an and to yield:

resulting statement 1: A and B --> C

or we could have diagrammed the original statement as

A--> (~C-->~B)
pulling the first term out and adding an and yields:

resulting statement 2: A and ~C --> ~B

I was expecting resulting statements 1 and 2 to be logically equivalent but they are not. Can anyone clarify why this is not the case? I would imagine this affects one's chances of correctly answering a question with an embedded conditional.

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Comments

  • blah170blahblah170blah Alum Inactive ⭐
    edited February 2015 3545 karma
    Deleted
  • arabprodigy30arabprodigy30 Alum Member
    243 karma
    "if A then no B unless C"

    From what I have been taught, (taken Kaplan prep course, but not nearly as helpful as JY)

    Whatever is before unless you negate it to its opposite

    so No B---> would become B

    If A->B->C
    If A and B ->C

    (my own question , why did you add the and?)

    But I think the contrapositive would then be

    Not C-> Not B->not A ?

    Don't think you can diagram as A--> (~C-->~B)
  • jdawg113jdawg113 Alum Inactive ⭐
    2654 karma
    well not too great at this stuff but that does look right. I think it's not the same just because of the () turning into the "and" statement. I think the transition causes issues when you look at it converted. Though as far as I can tell those translations look correct.

    @SoltanShah JY has a video where he goes through the steps of taking out the () which includes adding the and. Take a little time to look over what he put and see if you can tell how it makes sense. It is an equivalent way of saying the same thing as the first statement just without the parenthesis
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