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Hi all!
I just have a question regrading And + Or in the SC and NC and what happens when you Satisfy the SC through Valid Argument Form #1 and Deny the NC through Valid Argument Form #2. Here is where my thinking is at right now if any of you can correct me please do!!
Or in the Sufficient Condition
Valid Argument Form #1: Satisfying the Sufficient Condition
A or B --> C
Because it is an or statement there are three ways that can you can possibly satisfy the Sufficient Condition and conclude C.
Valid Argument Form #2: Denying the Necessary Condition
A or B --> C
When you deny the Necessary Condition by saying /C you can end up with 3 possibilities.
And in the Necessary Condition
Valid Argument Form #2: Denying the Sufficient Condition
A --> B and C
When you say /B and /C you conclude /A because B and C are jointly necessary they must both be denied.
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Valid Argument Form #2: Denying the Necessary Condition
A or B --> C
When you deny the Necessary Condition by saying /C you can end up with 3 possibilities.
A and /B
B and /A
/A and /B
In the above case, when you deny C, you must deny A AND deny B. So your #1 and #2 statements are not correct.
/C --> [/A AND /B]
It is also easier to break up OR in the sufficient condition like this:
A or B --> C
A --> C
B --> C
Therefore, when
/C --> /A
/C --> /B
and if you want to combine the above,
/C --> [/A AND /B]
(because AND in the necessary condition can be split)
Hope this makes sense and let me know if you have questions!
@drbrown2259 Ah i see thank you so much for the clarification. I just thought that because it was A --> B AND C that it requires that both the Necessary Conditions (B and C) be negated to get /A.
@99sav99sav106 said:
Hi all!
I just have a question regrading And + Or in the SC and NC
Or in the sufficient condition is sometimes easier mapped as 2 separate conditional statements.
A --> C , B -->C. Negating C would negate both A and B. With contrapositives of and/or statements you have to change the and/or to the opposite or/and.
So with that as a rule (De Morgan's Laws from CC), we need to fix up your description of and in the necessary condition.
A --> B and C. The contrapositive turns into an or in the sufficient conditions, which we can map into two separate conditional statements. /B or /C --> /A. /B --> /A because if A then B and C. /C --> /A because if A then B and C. You don't have to have both B and C negated to get not A.