A relation R(A,B,C,D) is given.
C and D are equivalent (C is the course ID and D is the course name, one implies the other).
C and D are prime attributes.
Does that violate the requirement of 1NF or any other NF?
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As I understand your description C and D are called candidate keys. Either one of them could be used alone as the key. The combination of them both cannot be a candidate keys as each is redundant to the other - given a course ID we know the course name, given a name we know the ID.
Let's say we choose C as the primary key. Then D
Had we chosen D as the primary key then C would be normalized by symmetrical arguments.