Select the correct properties of a Barrier function $B(x)$ from the following options.

a$.B(x)>0$AAxin$\frac{D}{\frac{?}{?}}{x}_0$

b$.B^{}(x)0AAn\frac{D}{\frac{?}{?}}U$

c$.B(x)<mn\; id="EditorElement\_189697">0</mn>$AAxin$\frac{D}{\frac{?}{?}}{x}_0$

d$.B^{}(x)0$AAxin$\frac{D}{\frac{?}{?}}U$

a$.$

b$.$

C$.$

d$.$