Is this table in third normal form?
Here's one attempt (this is not a day to day activity for me, so I may be doing some weird errors below):

A and B are clearly candidate keys of R. Therefore C is the only non-prime attribute of R

R is in 3NF iff:

a) R is in 2NF

b) Every non-prime attribute of R (C) is non-transitively dependent on every superkey of R.

The superkeys of R is (A, B), (A, C), (A, B, C)

By reflexivity (A, C) -> C AND (A, B, C) -> C
By composition of A->C and B->C we get (A, B) -> (C, C), i.e. (A, B) -> C

C is therefore non-transitively dependent on every superkey of R, and hence R is in 3NF.