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Is this sentences correct ?

" My Business Administration Faculty is the first program as the university established "

( I want to explain that my B.A. faculty is the first program which was founded at the same time that the university established. It was born simultaneously with the university)

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If the sentence is wrong. Can I still use "As" in that sentence and how ?

Thank you.
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Do not use "as." You could use "that" instead:
My Business Administration Faculty is the first program that the university established.

Also, do you mean to include "faculty" (which more commonly refers to the teaching staff). I would drop the word entirely.

You can say your thought in a number of ways:

Business Administration was the first program created by the newly established university.

Business Administration was established at the same time as the university.

Business Administration is as old as the university.

I hope this helps.
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Thank you.