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We show that the following is a tautology:
((A \/ B) /\ (A => C) /\ (B => C)) => C.We assume that its truth value is false and then derive a contradiction:
((A \/ B) /\ (A => C) /\ (B => C)) => CBecause the implication is false, C is false and the conjuncts are true. Thus A and B must be false. Therefore A \/ B is false, which contradicts above derivation.