1. There are two books; one is mine, the other is my friend's.

2. There are two books; one is mine, and the other is my friend's.
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Is #1 correct? In Sentence 'and' is missing.

Yes, you are correct. Sentence #1 is missing the word "and" between "mine" and "the other." The correct sentence structure should be:

"There are two books; one is mine, and the other is my friend's."

To determine if a sentence is correct, you can double-check the grammar and punctuation. In this case, adding the conjunction "and" between "mine" and "the other" helps to properly connect the two parts of the sentence.