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Quick conditional question on contraspositives

I say go go goI say go go go Alum Member

Hello Everyone,

I wanted to know that if

A -> B + C (with the + being "and")

Then the Contra would be /B or /C -> /A

And in another situation

+ ====> D

/D ====> /A or /B?

Thank you!


  • Jay HawladerJay Hawlader Alum Member
    105 karma

    A nice trick to simplify I learned is that if “AND” is in the outcome (If A then B AND C) then you can separate them to be:

    A—> B
    A—> C

    If “AND” is in the trigger ( If A and B then C) then you have to keep them together

    A and B —> C

    Contrarily if “OR” is in the outcome (If A then B or C) then you have to keep the two together

    A—> B or C

    If “OR” is in the trigger (If A or B then C) then you can separate it


    This should make negating a few easier.

    Your example A—>B and C would negate into:

    /B or /C —> /A

    Or in other words:

    /B—> /A



    For the ones that have to stay together it would be like this:

    Original: A and B —> C
    Negation: /C —> /A or /B

    Original: A —> B or C
    Negation: /B and /C —> /A

    Hope this wasn’t confusing. Also typing on my phone so this was a bit challenging!

  • WouldratherbefishingWouldratherbefishing Alum Member
    40 karma

    Why is not D -> /A+B ?

  • Sally SallySally Sally Member
    169 karma

    @Wouldratherbefishing A+B->D is saying 'if we have the combination of A and B then we have D,' so the contrapositive is 'if there's no D, it must be that A and B weren't combined.' We would represent this by saying /D->/A or /B, which says if there's no D, either we have A but no B, have B but no A, or we have no A and no B

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