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Question:

Published on: 23 February, 2025

Write short notes on the following:

Armstrong’s Axioms

Outer join

Answer:

Armstrong’s Axioms:

An inference axiom is a rule that states if a relation satisfies certain Functional Dependencies (FDs) then it must satisfy certain other FDs. These rules are applied repeatedly for a give set of FDs so that all of F+ i.e. closure can be inferred. Let X, Y, Z, W be the arbitrary schema R and XY is denoted by XY.

F1. Reflexivity If Y Í X, then X →Y holds

F2. Augmentation If X → Y then XW → YZ

F3. Transitivity If (X → Y) and (Y → Z) then (X → Z)

Computing F+ using axioms directly is quite complicated. Thus, to simplify the task of computing F+ from F, additional inference rules are derived from Armstrong’s axioms. These rules are:

F4. Union If {(X → Y) (X → Z)} then X → YZ

F5. Decomposition If (X → YZ) then X → Y

F6. Pseudo-transitivity If (X → Y) and (YZ → W) then XZ → W

Outer Join:

Outer Join is based on both matched and unmatched data. Outer Joins subdivide further into,

Left Outer Join
Right Outer Join
Full Outer Join

R1: class R2: class info

ID	Address
1	DELHI
2	MUMBAI
3	CHENNAI
7	NOIDA
8	PANIPAT

ID	NAME
1	abhi
2	adam
3	alex
4	anu
5	ashish

Left Outer Join

The left outer join returns a result table with the matched data of two tables then remaining rows of the left table and null for the right table's column.

ID	NAME	ID	Address
1	abhi	1	DELHI
2	adam	2	MUMBAI
3	alex	3	CHENNAI
4	anu	null	null
5	ashish	null	null

Right Outer Join

The right outer join returns a result table with the matched data of two tables then remaining rows of the right table left table's columns.

ID	NAME	ID	Address
1	abhi	1	DELHI
2	adam	2	MUMBAI
3	alex	3	CHENNAI
null	null	7	NOIDA
null	null	8	PANIPAT

Full Outer Join

The full outer join returns a result table with the matched data of two table then remaining rows of both left table and then the right table.

ID	NAME	ID	Address
1	abhi	1	DELHI
2	adam	2	MUMBAI
3	alex	3	CHENNAI
4	anu	null	null
5	ashish	null	null
null	null	7	NOIDA
null	null	8	PANIPAT

Subjects

Data Structures & Algorithm Compiler Design Computer Graphics and Multimedia Software Engineering Database Management System C Programming and Practices

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