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| In [[relational algebra]], a '''generalized selection''' is a [[unary operation]] written as <math>\sigma_\varphi(R)</math> where <math>\varphi</math> is a [[propositional formula]] that consists of [[atomic formula|atom]]s as allowed in the [[selection (relational algebra)|normal selection]] and the logical operators <math>\and</math> ([[logical conjunction|and]]), <math>\or</math> ([[logical disjunction|or]]) and <math>\lnot</math> ([[negation]]). This selection selects all those [[tuple]]s in <math>R</math> for which <math>\varphi</math> holds.
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| For an example, consider the following tables where the first table gives the relation <math>Person</math> and the second the result of <math>\sigma_{Age \ge 30 \ \and \ Weight \le 60}(Person)</math>.
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| {| align="center" cellpadding="0" cellspacing="20"
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| ! <math>Person</math>
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| ! <math>\sigma_{Age \ge 30 \ \and \ Weight \le 60}(Person)</math>
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| |- style="vertical-align: top"
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| {| align="center" border="0" cellpadding="5" cellspacing="0" style="border-collapse: collapse; border: 1px solid black"
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| |- style="background-color: silver; text-align: left"
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| ! style="border: 1px solid black" | Name
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| ! style="border: 1px solid black" | Age
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| ! style="border: 1px solid black" | Weight
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| |-
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| | style="border: 1px solid black" | Harry
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| | style="border: 1px solid black" | 34
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| | style="border: 1px solid black" | 80
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| |-
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| | style="border: 1px solid black" | Sally
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| | style="border: 1px solid black" | 28
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| | style="border: 1px solid black" | 64
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| |-
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| | style="border: 1px solid black" | George
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| | style="border: 1px solid black" | 29
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| | style="border: 1px solid black" | 70
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| |-
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| | style="border: 1px solid black" | Helena
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| | style="border: 1px solid black" | 54
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| | style="border: 1px solid black" | 54
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| |-
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| | style="border: 1px solid black" | Peter
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| | style="border: 1px solid black" | 34
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| | style="border: 1px solid black" | 80
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| |}
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| {| align="center" border="0" cellpadding="5" cellspacing="0" style="border-collapse: collapse; border: 1px solid black"
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| |- style="background-color: silver; text-align: left"
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| ! style="border: 1px solid black" | Name
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| ! style="border: 1px solid black" | Age
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| ! style="border: 1px solid black" | Weight
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| |-
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| | style="border: 1px solid black" | Helena
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| | style="border: 1px solid black" | 54
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| | style="border: 1px solid black" | 54
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| |}
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| |}
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| Formally the semantics of the generalized selection is defined as follows:
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| : <math>\sigma_\varphi(R) = \{ \ t : t \in R, \ \varphi(t) \ \}</math>
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| The result of the selection is only defined if the [[Property (philosophy)|attribute]] names that it mentions are in the [[:wikt:heading|header]] of the relation that it operates upon.
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| The simulation of a generalized selection that is not a fundamental selection with the fundamental operators is defined by the following rules:
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| : <math>\sigma_{\varphi \and \psi}(R) = \sigma_\varphi(R) \cap \sigma_\psi(R)</math>
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| : <math>\sigma_{\varphi \or \psi}(R) = \sigma_\varphi(R) \cup \sigma_\psi(R)</math>
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| : <math>\sigma_{\lnot \varphi}(R) = R - \sigma_\varphi(R)</math>
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| The generalized selection is expressible with other basic algebraic operations.
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| In [[SQL]], general selections are performed by using <code>[[Where (SQL)|WHERE]]</code> definitions with <code>AND</code>, <code>OR</code>, or <code>NOT</code> operands in <code>[[Select (SQL)|SELECT]]</code>, <code>[[Update (SQL)|UPDATE]]</code>, and <code>[[Delete (SQL)|DELETE]]</code> statements.
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| ==See also==
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| * [[Selection (relational algebra)]]
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| [[Category:Relational algebra]]
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