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Given a universe of discourse <math>X,\!</math> suppose that <math>W \subseteq X</math> is the 1-adic relation, that is, the set, associated with the absolute term <math>\mathrm{w} = \text{woman}\!</math> and suppose that <math>L \subseteq X \times X\!</math> is the 2-adic relation associated with the relative term <math>\mathit{l} = \text{lover of}\,\underline{~~~~}.</math>
 
Given a universe of discourse <math>X,\!</math> suppose that <math>W \subseteq X</math> is the 1-adic relation, that is, the set, associated with the absolute term <math>\mathrm{w} = \text{woman}\!</math> and suppose that <math>L \subseteq X \times X\!</math> is the 2-adic relation associated with the relative term <math>\mathit{l} = \text{lover of}\,\underline{~~~~}.</math>
   −
The ''local flags'' of the relation <math>L\!</math> are given as follows:
+
Recalling a few definitions, the ''local flags'' of the relation <math>L\!</math> are given as follows:
    
{| align="center" cellspacing="6" width="90%"
 
{| align="center" cellspacing="6" width="90%"
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\\[6pt]
 
\\[6pt]
 
& = &
 
& = &
\text{the set of ordered pairs in}~ L ~\text{that have}~ u ~\text{in the 1st place}.
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\text{the ordered pairs in}~ L ~\text{that have}~ u ~\text{in the 1st place}.
 
\\[9pt]
 
\\[9pt]
 
L \star v
 
L \star v
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\\[6pt]
 
\\[6pt]
 
& = &
 
& = &
\text{the set of ordered pairs in}~ L ~\text{that have}~ v ~\text{in the 2nd place}.
+
\text{the ordered pairs in}~ L ~\text{that have}~ v ~\text{in the 2nd place}.
 +
\end{array}</math>
 +
|}
 +
 
 +
The ''flag projections'' of the relation <math>L\!</math> are defined this way:
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 +
{| align="center" cellspacing="6" width="90%"
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|
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<math>\begin{array}{lll}
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u \cdot L
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& = &
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\operatorname{proj}_2 (u \star L)
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\\[6pt]
 +
& = &
 +
\{ x \in X : (u, x) \in L \}
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\\[6pt]
 +
& = &
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\text{loved by}~ u.
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\\[9pt]
 +
L \cdot v
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& = &
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\operatorname{proj}_1 (L \star v)
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\\[6pt]
 +
& = &
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\{ x \in X : (x, v) \in L \}
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\\[6pt]
 +
& = &
 +
\text{lover of}~ v.
 
\end{array}</math>
 
\end{array}</math>
 
|}
 
|}
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