Rules of Implication: Is [(P implies A) etc] True?

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The discussion centers on the logical implications of the statement [(P implies ~A) and (P implies B) and (P implies C)]. It concludes that if this combination is deemed impossible, it does not necessarily validate the statement [(P implies A) and (P implies B) and (P implies C)]. The key point is that P cannot simultaneously imply both A and its negation ~A. Therefore, the implication does not hold true. The conversation highlights the complexities of logical relationships and their implications in formal reasoning.
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Suppose I know that [(P implies ~A) and (P implies B) and (P implies C)] is impossible. Does this means that the following statement is true: [(P implies A) and (P implies B) and (P implies C)]?

Any help is greatly appreciated!
 
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so basically you are asking if (P implies ~A) implies that (P implies A) and it does not..
 
I guess you're right! P cannot imply both A and ~A...
 

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