Quantum Mechanics-Spin State for Identical Particles

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Consider a system of two identical spin-1 particles. Find the spin states for this system that are symmetric or antisymmetric with respect to exchange of the two particles. (Problem 13.3, QUANTUM MECHANICS, David H. McIntyre)

I know that for bosons, the total wavefunction should be symmetric. Therefore, we can have symmetric or antisymmetric spin state. But are the possible spin states still |0,0> or |1,M>, which are for the spin-1/2 fermions? Any help will be appreciated! :smile:
 

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