Examples 7.2

Examples 7.2 - Examples 7.2 More Rules of Replacement...

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Examples 7.2 More Rules of Replacement! Constructive Dilemma (CD) (P Q) · (R S) P v R Q v S Here’s a short English equivalent, though, admittedly, we don’t use it much: If it rains then the game is cancelled, and if I miss the game then I’ll be unhappy. Either it rains or I miss the game. Therefore, either the game is cancelled or I’ll be unhappy. We can view this rule as a double modus ponens. If the first line is true, and if it’s true that we have P or R, too, then we’re going to have either Q or S necessarily. To think of it in terms of truth value, just imagine that one of the disjuncts of the second premise HAS to be true. If that’s the case (and it is), then one of the antecedents in the first premise has to be true, too. And, since both conjuncts up there have to be true, if one of the antecedents is true, then the corresponding consequent will be true, too (or else the conditional is false—and then so is the whole conjunction). Thus, if the second premise
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Examples 7.2 - Examples 7.2 More Rules of Replacement...

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