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On pg 118-119, where the LR Bible talks about Conditional Reasoning, the diagrams of Sufficient --> Necessary and A+ --> Study are somewhat confusing to me. After reading the analysis and understanding the concepts of valid, mistaken reversal, contrapositive, and mistaken negation, could I simply just remember the diagrams like this instead?


Valid = A → B
Mistaken Reversal = B → A
Contrapositive = -B → -A
Mistaken Negation = -A → -B

Is this accurate?

Correct.

Basically, in A -> B, A is the sufficient condition, B is the necessary condition.

I'll illustrate this with a common example:

Valid = A → B If it rained,then the ground is wet.

Mistaken Reversal = B → A would read If the ground is wet, then it rained. Clearly this is not necessarily true (e.g., someone could have pissed on the ground, etc).


Contrapositive = -B → -A would read If the ground is not wet, then it did not rain. This makes perfect sense (for the purposes of discussion, let's assume that nobody dried the ground and that we're talking about a time frame in which evaporation would not yet have dried the ground).

Mistaken Negation = -A → -B would read If it didn't rain, then the ground is not wet, which is not necessarily true (e.g., someone could have pissed on the ground, etc.).

Sounds good. Thank you very much!

notaznguy wrote:Valid = A → B
Mistaken Reversal = B → A
Contrapositive = -B → -A
Mistaken Negation = -A → -B

Is this accurate?

Yep.