For instance that the reflexive, transitive closure \(E^* x,y)\) of the edge relation of a graph \(G = \langle V,E \rangle\) as the smallest relation satisfying the condition \(E^* x,y)\) is thus definable as \ \text{Fix}((x = y) \vee E x,y) \vee \exists z(R x,z) \wedge R z,y))\).
For instance that the reflexive, transitive closure \(E^* x,y)\) of the edge relation of a graph \(G = \langle V,E \rangle\) as the smallest relation satisfying the condition \[ E^* x,y) \leftrightarrow [(x = y) \vee E x,y) \vee \exists z(E^* x,z) \wedge E^* z,y)] \] \(E^* x,y)\) is thus definable as \ \text{Fix}((x = y) \vee E x,y) \vee \exists z(R x,z) \wedge R z,y))\).
In a multivariate linear regression model adjusted for the clinical confounders used in model 1 and histopathological variables, diabetic retinopathy, HbA1c and eGFR were the variables with the smallest relation to the decrease in haemoglobin level (P = 0.85, 0.79 and 0.74, respectively); therefore, model 2 was devised by excluding diabetic retinopathy, HbA1c, and eGFR.
Andréka and Maddux [Notre Dame J. Formal Logic 35 (4) 1994] classified the small relation algebras those with at most 8 elements, or in other terms, at most 3 atomic relations.
It can be defined, equally circularly (because quantifying over all equivalence relations including itself), as the smallest equivalence relation (an equivalence relation being one which is reflexive, symmetric and transitive, for example, having the same shape).
The transitive closure of a relation R is the smallest transitive relation S which contains R. The transitive closure of a relation is sometimes also known as the ancestral of the relation.
Trust annotations in types are subjected to a subtyping relation (spreceq s'), meaning that trust type (s) is a subtype of (s'), which is defined as the smallest reflexive relation (encoded as an inductive type) such that (the only non-reflexive element of relation (preceq ) is ) tr(preceq )dis.
Often, it is denoted by (mathcal{R}^{s}). . the inverse (or transpose or dual) relation of (mathcal{R}), is defined as mathcal{R}^{-1}=bigl{ (x,y in X^{2}:(y,x inmathcal{R} bigr} mbox{ which is denoted by } mathcal{R}^{-1}; the symmetric closure of (mathcal{R}) is defined as the smallest symmetric relation containing (mathcal{R}) (i.e., (mathcal{R}^{s}:=mathcal{R}cupmathcal{R}^{-1})).
The only valuations that respect both these determinants are vT, assigning T to every formula, and vF assigning F to every formula, and the logic determined by {vT,vF} is the smallest trivial consequence relation on the language concerned.
In plots where the undergrowth is less dense, circular plots could be employed as having the smallest periphery in relation to area and consequently the lowest number of borderline trees [17].
In plots where the undergrowth is less dense, circular plots could be employed as having the smallest periphery in relation to area and consequently the lowest number of borderline trees [ 17].
