# Definition:Singular Conjunction

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## Definition

Let $\Bbb B = \set {\T, \F}$ be a boolean domain.

A **singular conjunction** in the set of propositions of type $\Bbb B^k \to \Bbb B$ is a conjunction of $k$ literals that includes just one conjunct of each complementary pair:

- $\set {x_j, \neg x_j}$

for each $j: 1 \le j \le k$.

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A singular proposition $s : \mathbb B^k \to \mathbb B$ can be expressed as a **singular conjunction**:

- $s = e_1 \land e_2 \land \ldots \land e_{k - 1} \land e_k$

where:

- $\forall j \in \closedint 1 k: e_j \in \set {x_j, \neg x_j}$

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