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Compounds with the same chemical formula and atom connectivity but differ in three-dimensional arrangement of atoms around the carbon atom are called stereoisomers.

They can be enentiomers or diastereisomers.

Stereoisomers that are mirror images of each other are called enantiomers. For a molecule having more than one chiral centre, the configuration of all the chiral centres will be different for enantiomers.

Diastereoisomers are stereoisomers that are not related as mirror images. Diastereoisomers have different configurations in only some chiral centres of the molecule.

The relative configuration of a sugar molecule is determined by comparing it with the R and S isomers of glyceraldehydes. If the lowest chiral carbon of the given sugar is similar to the R isomer of glyceraldehydes, it has D-configuration. A sugar isomer is considered an L-sugar if the bottom chiral carbon of sugar is similar to the S isomer of glyceraldehyde.

If the chiral carbon farthest from the carbonyl functional group has a hydroxyl group on the right side, it is a D-isomer. If the hydroxyl group is positioned to the left side, the sugar is an L-isomer.

(a) The given compounds are D-erythrose and L-erythrose.

Erythrose is an aldotetrose with two chiral centres at second and third carbon.

The isomer of erythrose in which the bottom chiral carbon has a hydroxyl group on the right side is D-erythrose and can be given as:

The isomer of erythrose in which the hydroxyl group of bottom chiral carbon is positioned to the left is called L-erythrose and is given by:

From the structures, it can be seen that the configuration of both the chiral centres of the compound is different, and they are mirror images.

Therefore, D-erythrose and L-erythrose are enantiomers.

(b) The isomers given are L-erythrose and L-threose

The structure of L-erythrose is given by:

Threose is aldotetrose with two chiral carbon. The isomer of threose with the hydroxyl group of the bottom chiral centre to the left is called L-threose.

The structure of L-threose is given by:

The structure shows that the configuration of only one chiral carbon is different, and they are not mirror images of each other.

Therefore, L-erythrose and L-threose are diastereoisomers.