Do you know a Smith? why a?
It is not asking do you know a specific Smith. It is asking do you know anyone who has the surname Smith.
A Smith: from the class of Smiths: a generic reference.
A) Smith is a very popular name in England; do you know any Smiths?
B) Yes, my friend John is a Smith: his full name is John Michael Smith.
I am not a teacher.
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