Question

What is union compatibility? Why do the UNION, INTERSECTION, and DIFFER. ENCE operations require that the relations on which they are applied be union compatible?

Short answer

Union compatibility refers to the equivalence in structure of two or more relations, meaning they have the same number of columns and the corresponding columns have the same or compatible domains. The UNION, INTERSECTION, and DIFFERENCE operations require union compatibility because they involve comparing or combining tuples from two or more relations, which would be unclear or impossible if the relations had different or incompatible structures.

Step-by-step solution

Define Union Compatibility

Union Compatibility in database refers to the equivalence in structure of two or more relations. These relations (or tables, in DB language) are said to be union compatible if they have the same number of columns and the corresponding columns have the same or compatible domains.

Explain need of Union compatibility for UNION operation

The UNION operation combines the tuples of two relations and removes any duplicates. This can only be done if the relations are union compatible, otherwise it would be unclear how to combine different or incompatible columns.

Explain need of Union compatibility for INTERSECTION operation

The INTERSECTION operation returns all common tuples from two relations. This requires the relations to have compatible structure (union compatibility) , to accurately identify the common tuples.

Explain need of Union compatibility for DIFFERENCE operation

The DIFFERENCE operation identifies the tuples that are present in one relation but not in the other. This requires the relations to be union compatible, otherwise it would be unclear how to compare each tuple from the relations.

Key concepts

UNION operation

The UNION operation is a fundamental process in databases to combine data. Think of it as mixing two sets of information to form a new set containing every item from both datasets without repeating any item. By performing a UNION operation, you ensure that a new dataset is created that includes every unique tuple from both original datasets.

In practical terms, if you have two tables of customer information, and you want to compile a comprehensive list without duplicates, UNION is your best friend. However, for UNION to work its magic, the two tables must be union compatible. This means:

• The tables must have the same number of columns.
• Corresponding columns should have the same or compatible data domains. This means data types should match.

Without union compatibility, a UNION operation would not be able to seamlessly combine the data, as mismatched columns would lead to confusion on how to merge the data successfully.

INTERSECTION operation

The INTERSECTION operation is used when you need to find commonalities between two datasets. Think about two circles overlapping in a Venn diagram; they share a space that represents the INTERSECTION. In database terms, this operation retrieves all tuples that appear in both sets.

To precisely identify these shared records, both datasets need to be union compatible. This requirement means:

• The datasets must have the same number of columns.
• These columns must match in data type to ensure accurate comparisons.

When datasets meet these criteria, it is straightforward to perform the INTERSECTION operation and extract the exact tuples that exist in both datasets. If the datasets are not union compatible, determining which records intersect would be problematic, possibly leading to inaccurate data collection.

DIFFERENCE operation

The DIFFERENCE operation helps unearth the unique elements of a dataset compared to another. It's similar to comparing two lists to find out what items exist in one but not the other. In databases, it is utilized to discover tuples existing in one dataset but missing in another.

This operation is crucial for tasks like determining what new entries have been added or which entries have been removed when comparing current versus previous datasets. However, for this operation to work, union compatibility is a must.

Union compatibility requires:

• Identical number of columns in each dataset.
• Corresponding columns with matching or compatible data types.

Without these structural similarities, executing a DIFFERENCE operation becomes challenging as the database system wouldn't know how to accurately compare the tuples from each dataset. This ensures that only true differences, based on comparable data, are revealed.