Can minimum relative humidity be greater than maximum relative humidity? I am trying to calculate minimum and maximum daily Relative Humidity values given a min/max Specific Humidity and min/max Temperature.

I found some equations here that work with the given variables, but I have noticed that occasionally the value calculated for Minimum Relative Humidity will be greater than the value calculated for Maximum Relative Humidity. Is this accurate? It feels incorrect that a lower specific humidity and temperature would lead to a higher relative humidity, and it also doesn't seem right to say that, for example, the minimum RH was 80% while the maximum RH was 50%. 

I verified my results with this online calculator, and while it is unclear what equations are being used here, the same scenario occurs.

Here are my C# functions for calculating RH. Specific Humidity is given as kg/kg, and Temperature in Celsius:

    public static double CalculateRHmin(double MinSpecificHumidity, double MinTemperature)
    {
        double RHmin = 0.0;
        double es = 6.112 * Math.Exp((17.67 * MinTemperature)/(MinTemperature + 243.5)); 
        double e = MinSpecificHumidity * 1013.25 / (0.378 * MinSpecificHumidity + 0.622);
        RHmin = 100 * (e / es);
        return RHmin;
    }

    public static double CalculateRHmax(double MaxSpecificHumidity, double MaxTemperature)
    {
        double RHmax = 0.0;
        double es = 6.112 * Math.Exp((17.67 * MaxTemperature) / (MaxTemperature + 243.5));
        double e = MaxSpecificHumidity * 1013.25 / (0.378 * MaxSpecificHumidity + 0.622);
        RHmax = 100 * (e / es);
        return RHmax;
    }


Sample execution:

Tmin(Celsius) = 12.71    SHmin(kg/kg) = 0.007672     RHmin = 84.71%

Tmax(Celsius) = 23.71    SHmax(kg/kg) = 0.010929     RHmax = 60.33%
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.