Tupple Relational Calculus is a **non-procedural query language** unlike relational algebra. Tupple Calculus provides only the description of the query but it does not provide the methods to solve it. Thus, it explains what to do but not how to do.

In Tupple Calculus, a query is expressed as

{t| P(t)}

where t = resulting tupples,

P(t) = known as Predicate and these are the conditions that are used to fetch t

Thus, it generates set of all tupples t, such that Predicate P(t) is true for t.

P(t) may have various conditions logically combined with OR (∨), AND (∧), NOT(¬).

It also uses quantifiers:

∃ t ∈ r (Q(t)) = ”there exists” a tuple in t in relation r such that predicate Q(t) is true.

∀ t ∈ r (Q(t)) = Q(t) is true “for all” tuples in relation r.

**Example:**

**Table-1: Customer**

Customer name | Street | City |
---|---|---|

Saurabh | A7 | Patiala |

Mehak | B6 | Jalandhar |

Sumiti | D9 | Ludhiana |

Ria | A5 | Patiala |

**Table-2: Branch**

Branch name | Branch city |
---|---|

ABC | Patiala |

DEF | Ludhiana |

GHI | Jalandhar |

**Table-3: Account**

Account number | Branch name | Balance | |
---|---|---|---|

1111 | ABC | 50000 | |

1112 | DEF | 10000 | |

1113 | GHI | 9000 | |

1114 | ABC | 7000 |

**Table-4: Loan**

Loan number | Branch name | Amount |
---|---|---|

L33 | ABC | 10000 |

L35 | DEF | 15000 |

L49 | GHI | 9000 |

L98 | DEF | 65000 |

**Table-5: Borrower**

Customer name | Loan number |
---|---|

Saurabh | L33 |

Mehak | L49 |

Ria | L98 |

**Table-6: Depositor**

Customer name | Account number |
---|---|

Saurabh | 1111 |

Mehak | 1113 |

Sumiti | 1114 |

**Queries-1:** Find the loan number, branch, amount of loans of greater than or equal to 10000 amount.

{t| t ∈ loan ∧ t[amount]>=10000}

Resulting relation:

Loan number | Branch name | Amount |
---|---|---|

L33 | ABC | 10000 |

L35 | DEF | 15000 |

L98 | DEF | 65000 |

In the above query, t[amount] is known as tupple variable.

**Queries-2:** Find the loan number for each loan of an amount greater or equal to 10000.

{t| ∃ s ∈ loan(t[loan number] = s[loan number] ∧ s[amount]>=10000)}

Resulting relation:

Loan number |
---|

L33 |

L35 |

L98 |

**Queries-3:** Find the names of all customers who have a loan and an account at the bank.

{t | ∃ s ∈ borrower( t[customer-name] = s[customer-name]) ∧ ∃ u ∈ depositor( t[customer-name] = u[customer-name])}

Resulting relation:

Customer name |
---|

Saurabh |

Mehak |

**Queries-4:** Find the names of all customers having a loan at the “ABC” branch.

{t | ∃ s ∈ borrower(t[customer-name] = s[customer-name] ∧ ∃ u ∈ loan(u[branch-name] = “ABC” ∧ u[loan-number] = s[loan-number]))}

Resulting relation:

Customer name |
---|

Saurabh |

## Recommended Posts:

- DBMS | Row oriented vs. column oriented data stores
- DBMS | Join operation Vs nested query
- Mathematics | Probability
- Functional Dependency and Attribute Closure
- DBMS | Relational Model Introduction and Codd Rules
- Database Management System - Introduction | Set 1
- Last Minute Notes - DBMS
- DBMS | How to solve Relational Algebra problems for GATE
- DBMS | How to solve Relational Algebra problems for GATE
- Basic Operators in Relational Algebra
- Extended Operators in Relational Algebra
- Database Management System | ER Model
- Database Normalization | Normal Forms
- Database Normalization | Introduction
- Database Management system | Relational Algebra

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.