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Dalaal March 2, 2020

Re-diagramming compound statements

I understood from prior explanations on the message board that A & B --> C is the same as or could be diagrammed as two separate general principles A --> C, B --> C. However, could you confirm that we can't do this when the conditional statement is A ---> B & C, i.e., we can't re-diagram it as A --> B, A ---> C, correct?

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SamA March 2, 2020

Hello @Dalaal,

I wonder if you may have misinterpreted some prior explanations on the message board. A & B - - - - -> C should not be diagrammed as two separate statements. If we did tell you that, then please direct me to the question so that I can fix it.

Because of the word "and," both sufficient conditions are needed to guarantee the necessary condition. One by itself is not enough.
We cannot conclude A - - - > C.

However, if your compound statement said A or B - - - - - -> C, then we could conclude A - - - - > C and B - - - - - > C. This is the difference between "and" and "or."

You wrote: A - - - -> B & C
You could logically conclude A - - - > B and A - - - > C. But remember that both must occur because your initial statement said "and." I'm not sure if it is helpful to divide that compound statement into two, but you are welcome to diagram in whatever way that makes sense to you. I'm not exactly sure what you mean by "re-diagram," but the initial diagram that you wrote should be good enough to demonstrate the logic.

Dalaal March 7, 2020

Can we state A - -> B or C is like stating A - - > B or A - - -> C

Ravi March 20, 2020

@Dalaal, I would not rewrite it like that. That's longer and provides more confusion. It also fails to easily show that happens if both B and C are out.

A-->B or C

The contrapositive for this is

Not B and not C-->not A

In order to conclude not A, Not B AND Not C have to happen in the sufficient. This isn't as apparent if you separate the statement as you did above.

Does this make sense? Let us know if you have any other questions!