$\backslash$table$[[2$b$,$Mole fraction and activity coefficient of component $1$ in the binary liquid,$3]]$ mixture is given by $x_1$ and ${}_1$ respectively. $G^E$ is excess molar Gibbs free energy of the mixture. $R$ is universal gas constant and $T$ is the absolute temperature of the mixture. Which one of the following is always true? Clarify your answer in one or two sentences.

A$)\underset{x11}{lim}{}_1=0$

B$)\underset{x11}{lim}\frac{GE}{RT}=0\mathrm{.}5$

C$)\underset{x11}{lim}{}_1=0\mathrm{.}5$

D$)\underset{x11}{lim}\frac{GE}{RT}=0$