Quick conditional question on contraspositives

Comments

• Jay Hawlader Alum Member

  September 2019 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
  And
  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

  A—>C
  B—>C

  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

  And

  /C—>/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!
• Wouldratherbefishing Member

  September 2019 40 karma

  Why is not D -> /A+B ?
• Sally Sally Member

  September 2019 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