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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
A
B
/D ====> /A or /B?
Thank you!
0
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
A
B
/D ====> /A or /B?
Thank you!
3 comments
@69469 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
Why is not D -> /A+B ?
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!