The up quark $u$ and down quark $d$ form a doublet ($u$, $d$). I know that they have a SU(2) symmetry. However, they also have a U(1) symmetry because they are regarded as two states of the same type of particle. I am puzzled: What is the symmetry of this doublet? Do they have two symmetries, i.e., SU(2) and U(1), or U(2) = SU(2) $\otimes$ U(1)? How to understand their symmetry?