Explanations:The sentence "They thought my brother had been involved in the crime, but was a case of _____ identity" requires a form of the verb "mistake" that fits grammatically and semantically. The correct form to use here is the past participle "mistaken."
To understand why "mistaken" is the correct choice, we need to look at the structure of the sentence and the role of the verb "mistake." The verb "mistake" can be used in various forms depending on the context. In this case, the sentence is describing a situation where someone was incorrectly identified as being involved in a crime. The phrase "was a case of" suggests that the sentence is referring to a completed action in the past, and it requires a form of the verb that indicates this past action.
The past participle form "mistaken" is used in passive constructions and after certain verbs like "be" or "have been." In the sentence, "mistaken" fits grammatically and semantically because it indicates that the brother was incorrectly identified as being involved in the crime. The sentence is essentially saying that the brother was not actually involved in the crime, but there was a mistake in identifying him as such.
Let's examine the other options to understand why they are incorrect:
Option A, "Mistook," is the simple past tense form of the verb "mistake." While it is a past form, it does not fit grammatically in the sentence because the sentence requires a past participle form to indicate a completed action in the past. The simple past tense form would be used in a different context, such as "They mistook my brother for someone else."
Option B, "Mistake," is the base form of the verb. It does not fit grammatically in the sentence because the sentence requires a past participle form to indicate a completed action in the past. The base form would be used in a different context, such as "They made a mistake in identifying my brother."
Option D, "Mistaking," is the present participle form of the verb "mistake." It does not fit grammatically in the sentence because the sentence requires a past participle form to indicate a completed action in the past. The present participle form would be used in a different context, such as "They were mistaking my brother for someone else."
Therefore, the correct form to use in the sentence is "mistaken," which is the past participle form of the verb "mistake." This form fits grammatically and semantically, indicating that the brother was incorrectly identified as being involved in the crime.