The defense proposes to show that the incident that the prosecution so _____________ rejects as _______ did indeed take place.

Option B is the correct answer.

"Cavalierly"< text> means in a dismissive or nonchalant manner, which aligns with the idea of the prosecution rejecting the incident with indifference. "Apocryphal" refers to something of doubtful authenticity, which fits the context of the prosecution dismissing the incident as something that is not believed to be true.

Option A: "Blithely" is too casual and doesn’t fit the strong rejection. "Undesirable" doesn’t capture rejecting something as false.

Option C: "Vehemently" works, but "factual" contradicts the rejection of the incident as false.

Option D: "Persuasively" doesn’t fit the prosecution’s rejection, and "pointless" doesn’t match the context.

Option E: "Convincingly" suits the defense, not the prosecution; "inevitable" doesn’t fit with rejection.