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Recalling the notion of semantic entailment, the relationship (p q) r, r p holds if, and only if, p computes to T whenever the formulas (p q) r and r evaluate to T. As done for tautology-checking, we ask whether this relationship can be violated. For that, p has to evaluate to F, while (p q) r and r evaluate to T. But this forces p and r to be true. Since this assignment of truth values makes (p q) r and r true and p false, we conclude that the condition for semantic entailment is indeed violated.
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