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If $f,g$ are two $\pm1$-valued functions and $f \lor g$ is their maximum (this is the standard notation for maximum; $\land$ stands for minimum), then $$f \lor g = \frac{1 + f + g - fg}{2}.$$ Since $\chi_S \chi_T = \chi_{S \Delta T}$, this shows that $$\chi_S \lor \chi_T = \frac{1}{2} + \frac{\chi_S}{2} + \frac{\chi_T}{2} - \frac{\chi_{S\Delta T}}{2}.$$ ...

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