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# Database Systems: Relational Algebra

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@RapidLimerick3617

### What is the main property of relational algebra operations?

They work on one or more relations to define another relation without changing the original relations

### What is represented by the Greek letter Sigma (σ)?

Selection operation

### What is the result of the set difference operation r - s?

The set of elements contained in r but not in s

### What is the purpose of the rename operator?

<p>To give a new name to a relation obtained after a relational algebra operation</p> Signup and view all the answers

### What is the Cartesian Product operation?

<p>A binary operator that takes two relations as input and associates every tuple of one relation with every tuple of the other</p> Signup and view all the answers

### What is the condition for applying the division operator?

<p>Attributes of B is a subset of A</p> Signup and view all the answers

### What is the result of the division operator?

<p>Tuples from relation A which are associated with every B’s tuple</p> Signup and view all the answers

### What is the symbol used to represent the join operation?

<p>⋈</p> Signup and view all the answers

### What type of join includes only those tuples that satisfy the matching criteria?

<p>Inner Join</p> Signup and view all the answers

<p>Theta Join</p> Signup and view all the answers

## Study Notes

### Relational Algebra

• Relational algebra operations work on one or more relations to define another relation without changing the original relations.
• Both operands and results are relations, so output from one operation can become input to another operation.
• Allows expressions to be nested, just as in arithmetic, which is called closure property.

### Basic Operations on Relations

• Selection: selects tuples that satisfy the given condition.
• Projection: returns its argument relation with specific attributes left out and removes duplicate rows.
• Union: combines two or more relations.
• Difference: returns the set of elements contained in one relation but not in another.
• Cartesian Product: associates every tuple of one relation with every tuple of another relation.
• Joins: combines two or more relations based on some conditions.

### Select Operation

• Represented with the lower case letter Sigma (σ).
• Selects tuples that satisfy the given condition.
• The input relation to the select operation is only one.

### Project Operation

• Represented with the letter π.
• Returns its argument relation with specific attributes left out.
• Removes duplicate rows.

### Union Operation

• Combines two or more relations.
• Relations must be union compatible (or type compatible).

### Set Difference Operation

• Returns the set of elements contained in one relation but not in another.
• Relations must be union compatible (or type compatible).

### Set Intersection Operation

• Returns the set of elements common to both relations.
• Relations must be union compatible (or type compatible).

### Cartesian Product Operation

• Associates every tuple of one relation with every tuple of another relation.
• Denoted by a cross symbol.
• Notation: r x s (all possible pairing).

### Rename Operator

• It is a unary operator (input is a single relation).
• It is used to give the name of our choice to a new relation obtained after using any linear algebra operation.
• Notation: ρ (R,E).

### Division Operator

• Used to find the tuples that are associated with every tuple of another relation.
• Notation: A/B or A ÷ B.
• Can be applied if and only if the attributes of B are a subset of A.

### Join Operation

• Combines two or more relations based on some conditions.
• It is a combination of Cartesian product and selection process.
• Join types: Inner Join, Outer Join (Left, Right, Full), Theta Join, Equijoin, Natural Join.

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## Description

Learn about relational algebra operations that work on one or more relations to define another relation, and how they can be nested like arithmetic expressions.

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