Show how the following experimental evidence can be used to deduce the structure of lactose (Section 22.12D):
1. Acid hydrolysis of lactose (C12H22O11) gives equimolar quantities of D-glucose and D-galactose. Lactose undergoes a similar hydrolysis in the presence of a β-galactosidase.
2. Lactose is a reducing sugar and forms a phenylosazone; it also undergoes mutarotation.
3. Oxidation of lactose with bromine water followed by hydrolysis with dilute acid gives D-galactose and D-gluconic acid.
4. Bromine water oxidation of lactose followed by methylation and hydrolysis gives 2, 3, 6-tri-O-methylgluconolactone and 2, 3, 4, 6-tetra-O-methyl- D-galactose.
5. Methylation and hydrolysis of lactose give 2, 3, 6-tri-O-methyl- D-glucose and 2, 3, 4, 6-tetra-O-methyl-d-galactose.