Step 1: Understanding the Task
The task is to identify the part of the sentence with a grammatical error.
Step 2: Analyzing Each Part
Part (a): "The respect that people have for science and for scientists' rests on the certain belief" - The use of "scientists'" with an apostrophe suggests possession, which doesn't fit here. It should probably be "scientists" (plural noun). However, the error in part (b) is more definitive. Let's re-examine part (a). While "scientists'" might be awkward, it's not as clear an error as in part (b). The primary error is elsewhere.
Part (b): "that science are the key to the understanding of the Universe and that" - This part contains a clear subject-verb agreement error. "Science" is a singular, uncountable noun. Therefore, it requires a singular verb. The verb "are" is plural. The correct verb is "is". The phrase should be "that science is the key...".
Part (c): "scientists can use science to manipulate that key." - This part is grammatically correct.
Step 3: Identifying the Error
The definitive error is in part (b). The singular subject "science" must be paired with the singular verb "is".
Step 4: Final Answer
The error lies in part (b). Therefore, option (B) is the correct answer.