D$-$Galactose is an isomer of D$-$talose

a$)$ Compare the reactivity of D$-$galactose and D$-$talose

b$)$ How can D$-$galactose be converted to D$-$talose? Propose the mechanism.

c$)$ Draw structures of $\backslash$beta $-$D$-$galactose and $\backslash$alpha $-$D$-$fructopyranose.

d$)$ How can Galactose$-$Talose and Talose$-$Galactose disaccharides be distinguished? Explain.

e$)$ D$-$Galactose can be converted to D$-$lyxose in two steps. In the first step, D$-$galactose is oxidized by bromine to form the intermediate that reacts with FeCl$3$ and H$2$O$2$ to produce D$-$lyxose. Propose mechanisms for both steps.