Relational Algebra

Question 1

Projection

Answer 1

• Extracts attributes from a relation
• pi_{attributes}(relation)

Question 2

Selection

Answer 2

• Selects tuples from a relation that match a predicate
• sigma_{predicate}(relation)

Question 3

Cartesian Product

Answer 3

• Forms a new relation containing all possible combinations of tuples from R_{1} with tuples from R_{2}
• R_{1} x R_{2}

Question 4

Natural Join

Answer 4

• Performs a filtered Cartesian product, removing tuples in which attributes with the same name have different values, and keeping only one copy of each duplicated column
• R_{1} |x| R_{2}

Question 5

Condition (Theta) Join

Answer 5

• Performs a filtered Cartesian product according to a specified predicate
• R_{1} |x|{Theta} R{2}

Question 6

Left Outer Join

Answer 6

• In addition to the natural-join tuples, include an extra tuple for each tuple from R_{1} with no match in R_{2}
• In the extra tuples, assign the R_{2} attributes NULL
• R_{1} -|x| R_{2}

Question 7

Right Outer Join

Answer 7

• In addition to the natural-join tuples, include an extra tuple for each tuple from R_{2} with no match in R_{1}
• In the extra tuples, assign the R_{1} attributes NULL
• R_{1} |x|- R_{2}

Question 8

Full Outer Join

Answer 8

• In addition to the natural-join tuples, include an extra tuple for each tuple from R_{2} with no match in R_{1}
• In the extra tuples, assign the R_{1} attributes NULL
• R_{1} -|x|- R_{2}

Question 9

Set Difference

Answer 9

• Select tuples that are in one relation but not the other
• The relations must have the same number of attributes
• Corresponding attributes must have the same domain
• R_{1} - R_{2}

Question 10

Assignment

Answer 10

• Assigns the result of an operation to a temporary variable or an existing relation
• Relation <– expression