Question Regarding And + Or

GUDETAMA

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.
1. A and /B
2. B and /A
3. A and B (Because unless otherwise specified we default to or as inclusive)

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.
1. A and /B
2. B and /A
3. /A and /B

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.

drbrown2

@"MY LEGGGGGGG" 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.

GUDETAMA

@drbrown2 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.

btownsquee

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.
1. A and /B
2. B and /A
3. /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!