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MyWikiBiz, Author Your Legacy — Saturday April 12, 2025
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* A '''singular boolean function''' ''s'' : '''B'''<sup>''k''</sup> → '''B''' is a boolean function whose fiber of 1 is a single point of '''B'''<sup>''k''</sup>.+* In the interpretation where 1 equals ''true'', a singular boolean function is called a '''singular proposition'''.+* Singular boolean functions and singular propositions serve as functional or logical representatives of the points in '''B'''<sup>''k''</sup>.+
; Boolean variable
; Boolean variable
−: A ''boolean variable'' <math>x\!</math> is a variable that takes its value from a boolean domain, as <math>x \in \mathbb{B}.</math>
+: A ''[[boolean variable]]'' <math>x\!</math> is a variable that takes its value from a boolean domain, as <math>x \in \mathbb{B}.</math>
; Proposition
; Proposition
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: When <math>1\!</math> is interpreted as the logical value <math>\operatorname{true},</math> then <math>f^{-1}(1)\!</math> is called the ''fiber of truth'' in the proposition <math>f.\!</math> Frequent mention of this fiber makes it useful to have a shorter way of referring to it. This leads to the definition of the notation <math>[|f|] = f^{-1}(1)\!</math> for the fiber of truth in the proposition <math>f.\!</math>
: When <math>1\!</math> is interpreted as the logical value <math>\operatorname{true},</math> then <math>f^{-1}(1)\!</math> is called the ''fiber of truth'' in the proposition <math>f.\!</math> Frequent mention of this fiber makes it useful to have a shorter way of referring to it. This leads to the definition of the notation <math>[|f|] = f^{-1}(1)\!</math> for the fiber of truth in the proposition <math>f.\!</math>
−; Singular boolean function
+: A ''singular boolean function'' <math>s : \mathbb{B}^k \to \mathbb{B}</math> is a boolean function whose fiber of <math>1\!</math> is a single point of <math>\mathbb{B}^k.</math>
−; Singular proposition
+: In the interpretation where <math>1\!</math> equals <math>\operatorname{true},</math> a singular boolean function is called a ''singular proposition''.
−: Singular boolean functions and singular propositions serve as functional or logical representatives of the points in <math>\mathbb{B}^k.</math>
* A '''singular conjunction''' in '''B'''<sup>''k''</sup> → '''B''' is a conjunction of ''k'' literals that includes just one conjunct of the pair <math>\{ x_j,\ \nu (x_j) \}</math> for each ''j'' = 1 to ''k''.
* A '''singular conjunction''' in '''B'''<sup>''k''</sup> → '''B''' is a conjunction of ''k'' literals that includes just one conjunct of the pair <math>\{ x_j,\ \nu (x_j) \}</math> for each ''j'' = 1 to ''k''.
