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Explain the following relational algebra operations with proper examples

The terms are

i. Natural join

ii. Assignment

iii. Rename

iv. Set-intersection operation

v. Union

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Natural join

Natural join is a type of inner join which is based on column having same name and same datatype present in both the tables to be joined.

Example:

Assignment

  • The assignment operation $(←)$ provides a convenient way to express complex queries
  • Write query as a sequential program consisting of a series of assignments followed by an expression whose value is displayed as a result of the query
  • Assignment must always be made to a temporary relation variable
  • Example: compute $r ÷s$
  • $temp1 ← ∏ R-S(r ), temp2 ← ∏ R-S((temp1 x s) –∏ R-S, S(r ))result = temp1 – temp2$
  • The result to the right of the ←is assigned to the relation variable on the left of the

Rename operation $( ρ )$

  • Results of relational algebra are also relations but without any name.
  • The rename operation allows us to rename the output relation. rename operation is denoted with small Greek letter rho ρ
  • Notation: $ρ x (E)$
  • Where the result of expression E is saved with name of x.

The set intersection operation

  • Finds tuples in both the relations.
  • It is denoted as ∩.

Example:

Borrower (customer-name, loan-number)

Depositor (customer-name, account-number)

Customer (customer-name, street-number, customer-city)

List all the customers who have both a loan and an account.

Code:

$Π$ customer-name (Borrower) $∩ Π$ customer-name (Depositor)

Union Operation $(∪)$

  • Union operation performs binary union between two given relations and is defined as
  • $r ∪ s ={ t | t ∈ r or t ∈ s}$
  • Notion: $r U s$
  • Where r and s are either database relations or relation result set (temporary relation).
  • For a union operation to be valid, the following conditions must hold:

r, s must have same number of attributes.

Attribute domains must be compatible.

Duplicate tuples are automatically eliminated.

$∏_{author}$ (Books) $∪∏_{author}$ (Articles)

Output: Projects the name of author who has either written a book or an article or both.

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