Option A: The longer the identifier, the more time it will take to scan the input string. Therefore, leading to more compilation time. Correct.
Option B: focus on the word necessary in the question. In simple language, option B can be paraphrased as
Longer identifiers in the program is a necessary condition for a program to be easier to understand which is equivalent to
If no longer identifiers in the program, the program is not easy to understand, the contrapositive of which is
If the program is easy to understand, it has longer identifiers.
The last implication is not a tautology. Hence option B is incorrect.
Conclusion: Option B can be made incorrect using mathematical logic.