The phrase "a relation on a" is correct and usable in written English.
It can be used in mathematical or logical contexts when discussing relationships defined on a set or structure.
Example: "In set theory, a relation on a set A is a subset of the Cartesian product A x A."
Alternatives: "a relation defined on a" or "a relation over a".
(DC) If (Rneqemptyset) is a relation on a set such that (operatorname{Range}(R) subseteq operatorname{Domain} (R)) then there is a function f with domain ω such that for all (ninomega), (( f ( n ),f ( n+1 ) ) in R).
It has been analyzed independently the performance of two structural forms of the generalized model, i.e., a relation depending on an integration of the properties of the solvent and the ionic salt and a relation on a reduced property-basis.
If ⊩ is such a relation on a language L then an L-valuation v is said to be consistent with ⊩ when there do not exist Γ, Δ, with v = T for all φ ∈ Γ and v = F for all ψ ∈ Δ.
A FOREACH operator with a "flatten" clause can expand one input tuple into a tuple list representing a relation on which relational operators can operate.
Let and be two vector spaces over a field, and let be a relation on both and.
Section 1 introduces the idea of formal sentential languages as (absolutely free) algebras, their primitive connectives having the status of the fundamental operations of these algebras, and explains the notion of a consequence relation on such a language.
Theorem 5.1 and Corollary 5.1 also hold if is a transitive relation on X, or a preorder on X, or a partial order on X.
For \(U \subseteq A\), let \(R\) be the binary relation on \(A + A = A \times \{0\} \cup A \times \{1\}\) given by It can be checked that \(R\) is an equivalence relation.
A binary relation on X is a nonempty subset (mathcal{R}) of (Xtimes X).
Definition 2.1 A binary relation on X is a nonempty subset ℛ of X × X.
A binary relation on X is a nonempty subset (mathcal{S}) of (Xtimes X).
