Relational Calculus

Tuple Relational Calculus

It is a non-procedural query language
This means that it will mention the required information without specifying the procedure to obtain it
An expression in tuple relational calculus is denoted as follows: {t | P(t)}
In other words, it is the set of all tuples t such that predicate P is true for t
t is a tuple variable and t[A] denotes the value of tuple t for attribute A
t $\in$ r denotes that tuple t is in relation r
The predicate can contain:
- A set of attributes and constants
- A set of comparison operators: (<, ≤, =, ≠, >, ≥)
- A set of connectives: and (∧), or (v)‚ not (¬)
- An implication (⇒): x ⇒ y, i.e. if x if true, then y is true
  x ⇒ y ≡ ¬x v y
- A set of quantifiers:
  $\exists$ t $\in$ r (Q (t)) ≡ "there exists" a tuple t in relation r such that predicate Q(t) is true
  $\forall$ t $\in$ r (Q (t)) ≡ Q(t) is true "for all" tuples t in relation r
Ex. Finding ID, name, dept_name and salary of all instructors who have salary greater than 80000: {t | t ∈ instructor ∧ t [salary] > 80000}

It is a non-procedural language as well
It is as powerful as tuple relational calculus
An expression in domain relational calculus is denoted as follows: {< $x_1, x_2, ... x_n$ >|P( $x_1, x_2, ..., x_n$ )}
where $x_1, x_2, ..., x_n$ are domain variables and P is the predicate
Ex. Finding ID, name, dept_name and salary of all instructors who have salary greater than 80000:
{<i, n, d, s> | <i, n, d, s> ∈ instructor ∧ s > 80000}

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Tuple Relational Calculus

It is a non-procedural query language

This means that it will mention the required information without specifying the procedure to obtain it

An expression in tuple relational calculus is denoted as follows: {t | P(t)}

In other words, it is the set of all tuples t such that predicate P is true for t

t is a tuple variable and t[A] denotes the value of tuple t for attribute A

t $\in$ r denotes that tuple t is in relation r

The predicate can contain:

A set of attributes and constants
A set of comparison operators: (<, ≤, =, ≠, >, ≥)
A set of connectives: and (∧), or (v)‚ not (¬)
An implication (⇒): x ⇒ y, i.e. if x if true, then y is true
x ⇒ y ≡ ¬x v y
A set of quantifiers:
$\exists$ t $\in$ r (Q (t)) ≡ "there exists" a tuple t in relation r such that predicate Q(t) is true
$\forall$ t $\in$ r (Q (t)) ≡ Q(t) is true "for all" tuples t in relation r

Ex. Finding ID, name, dept_name and salary of all instructors who have salary greater than 80000: {t | t ∈ instructor ∧ t [salary] > 80000}

Domain Relational Calculus

It is a non-procedural language as well

It is as powerful as tuple relational calculus

An expression in domain relational calculus is denoted as follows: {< $x_1, x_2, ... x_n$ >|P( $x_1, x_2, ..., x_n$ )}

where $x_1, x_2, ..., x_n$ are domain variables and P is the predicate

Ex. Finding ID, name, dept_name and salary of all instructors who have salary greater than 80000:

{<i, n, d, s> | <i, n, d, s> ∈ instructor ∧ s > 80000}