“Not that I know of.”
You are a receptionist in an office. An employee at the company asks if a package has come for her. No packages came while you were there, but you were gone for a couple hours. You say this because it's possible that it came while you were out.
Not that I know of.
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Use this phrase when you want to answer "no" to someone's question, but you're not 100% sure that "no" is really the correct answer.
Simply answering "no" makes it seem that you're completely sure that "no" is the correct answer. But if you answer "I don't know", it seems like you don't have any answer at all. "Not that I know of" falls in between. Another example:
A: Have any customers complained about the new application form?
B: Not that I know of.
Another version of this phrase is "none that I know of". For example:
A: Are there any good Indian restaurants around here?
B: None that I know of.