How are the following pairs of carbohydrates, shown in a Fischer projection, related to each other? Are they structural isomers, enantiomers, diastereomers, or epimers? Identify each as the d- or l-isomer. 
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Verified step by step guidance

1. Step 1: Understand the types of isomers involved. Structural isomers have different connectivity of atoms. Enantiomers are non-superimposable mirror images. Diastereomers are not mirror images and differ at one or more chiral centers. Epimers are a type of diastereomer that differ at only one chiral center.
2. Step 2: Identify the chiral centers in each carbohydrate. In a Fischer projection, chiral centers are typically the carbon atoms bonded to four different groups.
3. Step 3: Determine the configuration (D or L) of each carbohydrate. Look at the chiral center farthest from the carbonyl group (usually the bottom chiral center in a Fischer projection). If the hydroxyl group (-OH) is on the right, it is a D-isomer; if on the left, it is an L-isomer.
4. Step 4: Compare the configurations of the chiral centers in both carbohydrates. Check if they are mirror images (enantiomers), differ at one chiral center (epimers), or differ at multiple chiral centers but are not mirror images (diastereomers).
5. Step 5: Based on the comparison, classify the relationship between the two carbohydrates as structural isomers, enantiomers, diastereomers, or epimers.

Key Concepts

Structural Isomers

Structural isomers are compounds that have the same molecular formula but differ in the arrangement of atoms. This can include variations in the connectivity of the carbon skeleton or the functional groups attached. Understanding structural isomers is crucial for analyzing carbohydrates, as their different structures can lead to distinct properties and functions.

Stereoisomers

Stereoisomers are compounds that have the same molecular formula and connectivity but differ in the spatial arrangement of atoms. This category includes enantiomers, which are mirror images of each other, and diastereomers, which are not mirror images. Recognizing stereoisomers is essential for determining the specific relationships between carbohydrate pairs in Fischer projections.

D- and L- Isomers

D- and L- isomers refer to the configuration of chiral centers in carbohydrates, based on the orientation of the hydroxyl group on the penultimate carbon. The 'D' designation indicates that the hydroxyl group is on the right in a Fischer projection, while 'L' indicates it is on the left. Identifying these isomers is important for understanding the biological activity and classification of carbohydrates.