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Quick conditional question on contraspositives

Alum Member
211 karma

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
+ ====> D
B

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

Thank you!

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• 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
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!

• Alum Member
40 karma

Why is not D -> /A+B ?

• 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