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The spin singlet and triplet states of a two-electron double quantum dot can be used to form a logical qubit that combines fast manipulation and a spin readout mechanism. We demonstrate single-shot readout of the two-electron states of a Si/SiGe double quantum dot using a quantum-point-contact charge sensor and spin-to-charge conversion. From the statistics of multiple single-shot measurements, we find the lifetimes of the spin states as a function of in-plane magnetic field. The lifetimes of the singlet and T0 triplet are both ~10ms and insensitive to magnetic field. The T-triplet lifetime increases with magnetic field, reaching ~3s at 1T