The pattern "if p, then q; not p; therefore not q" is invalid because q may still be true even if p is false. This error is known as the fallacy of denying the antecedent. It mistakenly treats the conditional as though p were a necessary condition for q, which the original statement does not assert. Therefore the fallacy described is denying the antecedent.
Option A:
Option A, affirming, corresponds to affirming the consequent, a different fallacy with the form "if p, then q; q; therefore p". It does not match the structure that begins with "not p". Hence affirming is not correct here.
Option B:
Option B is correct because the erroneous step is to deny the antecedent p and then incorrectly deny the consequent q, assuming q depends exclusively on p. This misinterpretation of the conditional leads to an invalid inference.
Option C:
Option C, strengthening, is not a standard label for any recognised formal fallacy in this context and does not capture the problem of negating p. It therefore cannot be the answer.
Option D:
Option D, converting, might suggest swapping antecedent and consequent, but the structure in the stem is not about such reversal; it is about drawing an unwarranted negative conclusion from the denial of p. Thus converting is inappropriate.
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