Can minimum relative humidity be greater than maximum relative humidity?
I think you might be getting confused. There is relative humidity. If you put in different values, you will get different results. For instance, if you replace the variable names of one of your functions (say replace Min with Max), you will have the same exact function.
Relative humidity is a ratio of the amount of water vapor in the air to the amount of water vapor that could be in the air (saturation vapor pressure $e_s$): $$RH=100\%\times\frac{e}{e_s}$$ Since the saturation vapor pressure decreases with increasing temperature (Clausius Clapeyeron equation):$$e_s=611 \exp\left(\frac{L_v}{R_v}\left[\frac{1}{273.15}-\frac{1}{T}\right]\right)$$ it is conceivable, and also not uncommon, for the maximum relative humidity to occur when the temperature and specific humidity is at a minimum.
So can the minimum relative humidity be greater than the maximum relative humidity? By definition of minimum and maximum, no. But the times that the minimum and maximum relative humidity occur are often counter-intuitive.