The correct way of writing is Neither Kim nor Shelby is to go into the cave.
When two or more things are false or won't happen, neither/nor are used together. For instance, neither the blue nor the red options are offered in size 4. Before noon, I won't give you a call or send you a message.
Neither of them is grammatically sound. Both express agreement in response to a statement made by a different speaker. Me neither means I disagree with the statement, and I either mean I agree with the statement. Almost primarily used in America is the phrase "Me either."
Both the words neither and nor are used to convey a negative, however, neither is always used before nor. However, neither of these may be employed by themselves in a sentence. Sentences that begin with "neither of" illustrate this.
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