What Denying the consequent is
In logic, denying the consequent is a form of argument in which one infers that the contrapositive of a conditional statement is true by assuming that the inverse of the original conditional statement is false. This is also known as modus tollens. Denying the consequent takes the form of:
If P then Q Not Q Therefore, Not P
Steps for Denying the Consequent:
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Identify the conditional statement: The statement should be in the form of an “if…then” statement, such as “If P then Q”.
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Identify the consequent: The consequent is the part of the statement that follows the “then”, in this case, Q.
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Negate the consequent: This can be done by using the word “not” or a negative word such as “no” or “never”.
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Draw the conclusion: The conclusion can be drawn by using the contrapositive of the statement, which is “not P”. This means that if the consequent is false, then the antecedent must also be false.
Examples
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If the probability of a coin flip resulting in heads is 0.8, then it is not true that the probability of a coin flip resulting in tails is 0.2.
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If a population is normally distributed, then it is not true that the mean is equal to the median.
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If a sample size is large enough, then it is not true that the sample mean is not a good estimator of the population mean.