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.]
----------------------------------------------------------------------------------
Does #5 mean #6 alone? Can #5 mean #7 or #8 according to the context?
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.
In the given sentences, let's break them down to understand their meanings and relationships:
#1: "She is the principal of our school."
This sentence means that there is a person who holds the position of principal at our school.
#2: "She is the principal whom I met before."
This sentence suggests that the speaker has met the principal at some point in the past. It does not necessarily imply that she is the only principal.
#3: "She is the only principal of our school."
This sentence means that there is only one principal at our school, implying that there are no others holding the same position.
#4: "She is the only principal whom I met before."
This sentence combines the ideas from sentences 2 and 3, meaning that the speaker has met the only principal of the school.
To answer your first question, sentence #1 (#3) refers to having a principal at the school, while sentence #2 does not necessarily mean the same as sentence #4. Sentence #2 only implies that the speaker has met the principal before, whereas sentence #4 implies that the person they met is the only one in that role.
Now let's move on to the next set of sentences:
#5: "He is the student of our school."
This sentence means that there is a person who is a student at our school. It does not necessarily imply anything about the uniqueness or any specific characteristics of the student.
#6: "He is the only student of our school."
This sentence means that there is only one student at our school, suggesting that there are no other students enrolled.
#7: "He is the student whom I like at our school."
This sentence implies that the speaker has a liking or preference for this particular student in the context of other students at the school. It does not necessarily mean that he is the only student.
#8: "He is the most famous student of our school."
This sentence implies that among all the students at the school, he is the most well-known or renowned. It does not mean he is the only student.
To answer your second question, sentence #5 (#6) refers to there being a student at the school, while sentences #7 and #8 provide additional information about the student based on the context. In the right context, sentence #5 could mean #7 or #8 if the liking or fame of the student is being emphasized. However, by itself, sentence #5 typically does not explicitly convey those meanings.