When the gum of the shrub Sterculia setigera is subjected to acidic hydrolysis, one of the water soluble components of the hydrolysate is found to be tagatose. The following information is known about tagatose:

(1) Molecular formula C₆H₁₂O₆.

(2) Undergoes mutarotation.

(3) Does not react with bromine water.

(4) Reduces Tollens reagent to give D-galactonic acid and D-talonic acid.

(5) Methylation of tagatose (using excess CH₃I and Ag₂O) followed by acidic hydrolysis gives 1,3,4,5-tetra-O-methyltagatose.

(a) Draw a Fischer projection structure for the open-chain form of tagatose.

(b) Draw the most stable conformation of the most stable cyclic hemiacetal form of tagatose.