The reasoning structure in the question is: IF A runs AND B will certainly not run, then A is the only one running. However, A and B may NOT be the only runners (other candidates), hence the reasoning is flawed.
The reasoning structure in the questions are:
A) IF A (Brown's) will not run AND B (New large stores) will certainly not run, then there are NO runners. Incorrect because the reasoning structure is different from question.
B) IF A (Saturday) runs AND B (Friday) will certainly not run, then A (Saturday) is the only one running. However, A (Saturday) and B (Friday) may NOT be the only runners (other weekdays), hence the reasoning is flawed. Correct because the reasoning structure is similar to the question.
C) IF A (Marilyn) runs AND B (Sven) will probably not run, then A (Marilyn) is probably the only one running. Incorrect because the reasoning structure in question requires certainty.
D) IF A (Rustimann) runs AND B (Jones) will certainly not run, then A (Rustimann) is the only one running. However, A and B ARE the only runners. Incorrect because the reasoning structure in question allows the possibility that A and B may not be the only runners.
E) IF A (this book) runs AND B (that other one) will certainly not run, then A is the only one running. However, A is the only runner (unlike running candidates where there can be many, there can only be one best book). Incorrect because the reasoning structure in the question allows the possibility that A and B may not be the only runners.