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Discuss problems with my premises..

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Seriously? Your logic is valid, of course. I'll discuss your premises briefly:

¬P
¬Q
¬R

¬[](P --> Q)
¬[](¬R --> ¬Q)

( "[]" = "necessarily" )

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I don't even see why we need the modality--I would think:

~(P --> Q)

and

~(~R --> ~Q)

are both true.