1. She is the principal of our school.

2. She is the principal whom I met before.
3. She is the only principal of our school.
4. She is the only principal whom I met before.
[#1 means #3, right? What about #2? #2 doesn't seem to be #4, does it?]

5. He is the student of our school.
6. He is the only student of our school.
7. He is the student whom I like at our school.
8. He is the most famous student of our school. [There are a great number of students in our school. Among them, he is the most famous student of our school.]
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Does #5 mean #6 alone? Can #5 mean #7 or #8 according to the context?

1 answer

1 -- This could mean the same as 3, but it could also just mean she's the principal right now (and there have been others in the past).
3 -- This could mean she's the only principal right now or that she's the only principal the school has ever had.

2 and 4 -- There may have been other principals, but she's the one (the only one?) I have ever met.

5 and 6 mean that the school has only one student, and he is it!

7 is different; it means, out of all the students in the school, he's the only one I like.

8 -- Your analysis of 8 is correct.