The correctly capitalized sentence is 'My mother was born in the great city of San Francisco.'
My mother was born in the great city of San Francisco.
The sentence that uses the rules of capitalization correctly is the one provided in the question. In this sentence, the proper nouns 'mother' and 'San Francisco' are capitalized, following the guidelines for capitalizing proper nouns, names of places, and titles. Additionally, the first word of the sentence 'My' is capitalized, adhering to the rule of capitalizing the first word of a sentence.
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