What Denying the antecedent is
In logic, denying the antecedent is a form of logical inference in which an antecedent (the “if” part of an “if-then” statement) is denied, and the consequent (the “then” part of the statement) is also denied. This is done by assuming the opposite of the antecedent and then concluding that the consequent is false.
For example, if we have the statement “If it is raining, then the ground is wet”, then denying the antecedent would be to assume that it is not raining and then conclude that the ground is not wet.
Steps for Denying the Antecedent:
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Identify the “if-then” statement in question.
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Negate the antecedent.
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Conclude that the consequent is false.
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Validate the conclusion.
Examples
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A survey found that 80% of people who own a pet also own a car. Denying the antecedent would be stating that, since not all people own a car, not all people own a pet.
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A study found that 90% of people who have a college degree earn more than $50,000 per year. Denying the antecedent would be stating that, since not all people have a college degree, not all people earn more than $50,000 per year.