Final answer:
β-galactosidase converts some lactose to allolactose, facilitating the metabolism of lactose in E. coli by inducing the lac operon.
Step-by-step explanation:
β-galactosidase is an enzyme that not only catalyzes the hydrolysis of lactose into glucose and galactose but also converts some lactose to allolactose. Lactose is a disaccharide consisting of β-D-galactopyranosyl-(β-1→4)-α-D-glucopyranose, which is commonly known as milk sugar. During the digestion process in E. coli, the conversion of lactose to allolactose is a critical step that triggers the induction of the lac operon, enabling the cell to metabolize lactose when glucose is not readily available.