Two spin-1/2 particles either are part of a spin-1 triplet or a spin-0 singlet. The singlet is antisymmetric but bosons need to be symmetric wave functions.
So does the spatial part of the wave function need to be antisymmetric in the singlet and symmetric in the triplet? What if we're only considering the spin state, how can we have both symmetric and antisymmetric spins? Please answer both questions. Thanks