+-- {: .rightHandSide} +-- {: .toc .clickDown tabindex="0"} ### Context #### Relations +-- {: .hide} [[!include relations - contents]] =-- #### Constructivism, Realizability, Computability +-- {: .hide} [[!include constructivism - contents]] =-- =-- =-- \tableofcontents ## Idea A relation in which either it or its negation is true. ## Definition A decidable [[binary relation]] $R$ on a set $S$ is a relation such that for all elements $a \in S$ and $b \in S$, $R(a, b)$ or $\neg R(a, b)$. ## Examples * Every set with [[decidable equality]] has a decidable equality relation. * In the presence of [[excluded middle]], every relation is a decidable relation. ## See also * [[decidable equality]] * [[stable relation]]