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denying the antecedent

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In conditional reasoning, arguing invalidly from a hypothetical proposition of the form If p then q that, because p is false, therefore q is false. For example, given the proposition If the burglars entered by the front door, then they forced the lock, it is invalid to deduce from the fact that the burglars did not enter by the front door that they did not force the lock. Compare affirming the antecedent, affirming the consequent, denying the consequent.

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