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In the below two sentences, can we exchange between 'up' and 'down.'?

If we can't, that means there are difference between up and down. Can you tell me the difference?

a. I went up to the teacher’s table.

b. I went down to my office in the city.
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a. I went up to the teacher’s table. -- 'Down' will not work here, since the teacher's table is at the top or head of the classroom.
b. I went down to my office in the city.-- If the speaker lives in the south side of the city, he may well go up to his office; some people go uptown, but most people go downtown.
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Comments  
It's nice to get your answer.
Thanks. Mister Micawber.